symbolic dynamics and characterization of complexity abstract symbolic dynamics deals with robust properties of dynamics without digging into numbers for one dimensional maps there have been some new results periodic window theorem generalized composition rule construction of median words without using harmonics and antiharmonics incorporation of discrete symmetry to analyze symmetry breaking and symmetry restoration etc this new understanding has been applied to ordinary differential equations in particular the systematics of stable periodic solutions in the lorenz model has been shown to be given basically by symbolic dynamics of the cubic map symbolic dynamics may be used to extract invariant characteristics from time series its relation with grammatical complexity will also be commented on

functional equations for circle homeomorphisms with golden ratio rotation number the investigation of a scaling limit for mappings of the circle to itself with golden ratio rotation number leads to a pair of functional equations with at least a formal resemblance to the functional equation using the accumulation of period doubling bifurcations we discuss the general theory of these functional equations assuming that solutions exist

sharkovskii s order for the appearance of superstable cycles in one parameter families of simple real maps an elementary proof we give an elementary proof of a theorem a la sharkovskii which orders according to the period the first occurrence of superstable cycles in some one parameter families of endomorphisms of the real line

a dual element based geometric element transformation method for all hexahedral mesh smoothing abstract due to their increased complexity hexahedral elements are more challenging with respect to mesh generation and mesh improvement techniques than tetrahedral elements in particular there is a lack of geometry based all hexahedral smoothing methods for mesh quality improvement being easy to implement practicable and efficient the recently introduced geometric element transformation method represents a new promising element oriented smoothing concept to resolve this deficiency by giving a dual octahedron based regularizing transformation this new approach is adapted in order to smooth all hexahedral meshes first numerical tests indicate that the resulting smoothing method yields high quality results at least comparable to those of a state of the art global optimization based approach while being significantly faster

an embedding of the farey web in the parameter space of simple families of circle maps we describe an embedding of the farey web an extension of the better known farey tree in the parameter space of simple families of circle maps we also discuss some consequences of this embedding on the organization of frequency locking and on topological properties of the boundary between simple and complicated dynamics

hypermeander of spirals local bifurcations and statistical properties in both experimental studies and numerical simulations of waves in excitable media rigidly rotating spiral waves are observed to undergo transitions to complicated spatial dynamics with long term brownian like motion of the spiral tip this phenomenon is known as hypermeander in this paper we review a number of recent results on dynamics with noncompact group symmetries and make the case that hypermeander may occur at a codimension two bifurcation from a rigidly rotating spiral wave our predictions are based on center bundle reduction sandstede scheel and wulff and on central limit theorems and invariance principles for group extensions of hyperbolic dynamical systems these predictions are confirmed by numerical simulations of the center bundle equations

on the resonance structure in a forced excitable system the dynamics of forced excitable systems are studied analytically and numerically with a view toward understanding the resonance or phase locking structure in a singular limit the system studied reduces to a discontinuous flow on a two torus which in turn gives rise to a set valued circle map it is shown how to define rotation numbers for such systems and derive properties analogous to those known for smooth flows the structure of the phase locking regions for a fitzhugh nagumo system in the singular limit is also analyzed a singular perturbation argument shows that some of the general results persist for the nonsingularly perturbed system and some numerical results on phase locking in the forced fitzhugh nagumo equations illustrate this fact the results explain much of the phase locking behavior seen experimentally and numerically in forced excitable systems including the existence of threshold stimuli for phase locking the results are compared with known results for forced oscillatory systems

medial axis transformation of a planar shape the medial axis transformation is a means first proposed by blum to describe a shape in this paper we present a 0 n log n algorithm for computing the medial axis of a planar shape represented by an n edge simple polygon the algorithm is an improvement over most previously known results interms of both efficiency and exactness and has been implemented in fortran some computer plotted output of the program are also shown in the paper

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

rotation interval from a time series a very useful concept for two frequency dynamical systems is the rotation interval a method is proposed and tested numerically for estimating it from a time series

mesh refinement via bidirected flows modeling complexity and computational results we investigate a problem arising in the computer aided design of cars planes ships trains and other motor vehicles and machines refine a mesh of curved polygons which approximates the surface of a workpiece into quadrilaterals so that the resulting mesh is suitable for a numerical analysis this mesh refinement problem turns out to be strongly np hard in commercial cad systems this problem is usually solved using a greedy approach however these algorithms leave the user a lot of patchwork to do afterwards we introduce a new global approach which is based on network flow techniques abstracting from all geometric and numerical aspects we obtain an undirected graph with upper and lower capacities on the edges and some additional node constraints we reduce this problem to a sequence of bidirected flwo problems or equivalently to b matching problems for the first time network flow techniques are applied to a mesh refinement problem this approach avoids the local traps of greedy approaches and yields solutions that require significantly less additional patchwork

finite volume distance field and its application to medial axis transforms accurate and efficient computation of the nearest wall distance d or level set is important for many areas of computational science engineering differential equation based distance level set algorithms such as the hyperbolic natured eikonal equation have demonstrated valuable computational efficiency here in the context as an auxiliary equation to the main flow equations the eikonal equation is solved efficiently with two different finite volume approaches the cell vertex and cell centered the application of the distance solution is studied for various geometries moreover a procedure using the differential field to obtain the medial axis transform mat for different geometries is presented the latter provides a skeleton representation of geometric models that has many useful analysis properties as an alternative to other methods the current d mat procedure bypasses difficulties that are usually encountered by pure geometric methods e g the voronoi approach especially in three dimensions and provides better accuracy than pure thinning methods it is also shown that the d mat approach provides the potential to sculpt control the mat form for specialized solution purposes

some flesh on the skeleton the bifurcation structure of bimodal maps abstract one of the main tools in the numerical study of two parameter families of one dimensional maps is the drawing of curves in parameter space corresponding to the existence of superstable periodic orbits we use kneading theory to describe the structure of these sets of curves for the case of maps with at most two turning points then we explain how the bifurcation structure hangs on this skeleton

a numerical study of the likelihood of phase locking abstract we report the results of numerical computation of the size of the set of s for which the hemeomorphism of the circle f k x x k 2 sin 2 x mod 1 is phased locked for values of k ranging from 0 1 to 1 the results suggest that for moderate values of k phase locking is unlikely except for small periods but that for k 1 almost all s give phase locking with large periods accounting for a surprisingly large portion of the total

on the existence of feigenbaum s fixed point we give a proof of the existence of ac2 even solution of feigenbaum s functional equation g text x lambda 0 1 g text g lambda 0 x g text 0 1 whereg is a map of 1 1 into itself it extends to a real analytic function over

the set of maps f_ ɑ b x x ɑ b 2π sin 2πx with any given rotation interval is contractible consider the two parameter family of real analytic maps f b x x b 2 sin 2 x which are lifts of degree one endomorphisms of the circle the purpose of this paper is to provide a proof that for any closed interval i the set of maps f b whose rotation interval is i form a contractible set

universality and self similarity in the bifurcations of circle maps abstract the bifurcation structure in a two parameter family of circle maps is considered these maps have a topological degree that may be different from one a generalization of the rotation number is given and symmetries of the bifurcations in parameter space are described continuity arguments are used to establish the existence of periodic orbits by plotting the locus of parameter values associated with superstable cycles self similar bifurcations are found these bifurcations are a generalization of the familiar period doubling cascade in maps with one extrema to two parameter maps with two extrema finally a scheme for the global organization of bifurcation in these maps is proposed

scopes reduction and morita equivalence classes of blocks in finite classical groups ii abstract we extend our work of j algebra 230 2000 378 423 on unipotent blocks of classical groups to blocks of orthogonal groups containing characters labelled by degenerate symbols we also show that for classical groups in the linear prime case there are only finitely many morita types of unipotent blocks with a given defect group

dissecting shrimps results for some one dimensional physical models this paper describes how certain shrimp like clusters of stability organize themselves in the parameter space of dynamical systems clusters are composed of an infinite affine similar repetition of a basic elementary cell containing two primary noble points a head and a tail defining an axis of approximate symmetry knowledge of the axis and the skewness of the k periodic main cell of a k 2 cluster is enough to define the orientation of the whole cluster in space peculiarly simple directions along which shrimp like clusters align are formed by the locus of doubly degenerate saddle zero multipliers corresponding to the main shrimp head in addition we report a family of models having the boundaries of all isoperiodic domains of stability totally degenerate and describe different aspects of their mathematical arrangement and some of their consequences for example that shrimps are diffeomorphic copies of shrimps

a genealogy for finite kneading sequences of bimodal maps on the interval we generate all the finite kneading sequences of one of the two kinds of bimodal map on the interval building each sequence uniquely from a pair of shorter ones there is a single pair at generation 0 with members of length 1 concomitant with this genealogy of kneading sequences is a unified genealogy of all the periodic orbits see figure 0

hexahedral meshing using midpoint subdivision and integer programming abstract the generation of finite element meshes of 3d hexahedral elements can be performed by subdividing the model into a number of simple bodies like hexahedra triangular prisms etc within these bodies regular or simple transition meshes can be generated in this paper a method called midpoint subdivision will be discussed which enables the user to build the model using a number of high level subregions which satisfy certain simple topological conditions these subregions can be automatically subdivided into meshes of hexahedral elements for analysis the distribution of elements within the mesh is typically controlled by specifying the division numbers of certain edges however for a given set of subregions there are a number of constraints on the edge division numbers that will yield a compatible mesh the use of integer programming will be discussed this finds the compatible division numbers which are nearest to but not less than the target values specified

complete devil s staircase fractal dimension and universality of mode locking structure in the circle map it is shown numerically that the stability intervals for limit cycles of the circle map form a complete devil s staircase at the onset of chaos the complementary set to the stability intervals is a cantor set of fractal dimension d 0 87 this exponent is found to be universal for a large class of functions

quasiperiodicity in dissipative systems a renormalization group analysis abstract dynamical systems with quasiperiodic behavior i e two incommensurate frequencies may be studied via discrete maps which show smooth continuous invariant curves with irrational winding number in this paper these curves are followed using renormalization group techniques which are applied to a one dimensional system circle and also to an area contracting map of an annulus two fixed points are found representing different types of universal behavior a trivial fixed point for smooth motion and a nontrivial fixed point the latter representsthe incipient breakup of a quasiperiodic motion with frequency ratio the golden mean into a more chaotic flow fixed point functions are determined numerically and via an e expansion and eigenvalues are calculated

universal properties of the transition from quasi periodicity to chaos in dissipative systems abstract an exact renormalization group transformation is developed for dissipative systems which describes how the transition to chaos may occur in a continuous and universal manner if the frequency ratio in the quasi periodic regime is held at a fixed irrational value our approach is a natural extension of k a m theory to strong coupling most of our analysis is for analytic circle maps we have found a strong coupling fixed point where invertibility is lost which describes the universal features of the transition to chaos we find numerically that any two such critical maps with the same winding number are c 1 conjugate it follows that the low frequency peaks in an experimental spectrum are universal and we determine how their envelope scales with frequency when the winding number has a periodic continued fraction our renormalization transform has a fixed point and spectra are self similar in addition for a set of non periodic winding numbers with full measure our renormalization transformation yields an ergodic trajectory in a sub space of all critical maps physically one finds singular and universal spectra that do not scale

renormalization in a circle map with two inflection points abstract an extended version of the sine circle map becomes non invertible by developing simultaneously two critical points in part of parameter space universality in the corresponding transition from quasiperiodicity to chaos manifests itself in the organisation of doubly superstable orbits four operators are needed to generate all such orbits the existence of non trivial equivalence relations for operation sequences makes the present theory different from other multi operator renormalisation approaches possible implications of the theory in higher dimensional systems are discussed

symbolic dynamics and skeletons of circle maps a circle map maps the circumference of a circle into itself such maps are of physical and biological interest because they arise naturally in many circumstances as for example the periodic forcing of limit cycle oscillators the canonical example of circle maps is x tx a sin2 x mod 1 where a and are two constants t is an integer that gives the topological degree of cycles that contain extremal points of are stable and are called superstable cycles the locus of superstable cycles in a parameter space is called the skeleton the critical points of x 0 and the discontinuous points of x 1 break into monotonic branches in this paper we propose a novel notation for symbolically representing the branches of x and discuss the symbolic sequences for the skeleton simple rules based on continuity of periodic orbits as parameters change allow us to construct the skeleton associated with all periodic orbits for the circle maps with t 0 0 a 1 0 and t 1 0 a 1 0 recursion formulae to compute the numbers of periodic orbits for t 0 and t 1 at 0 are given

a digraph based hexahedral meshing method for coupled quasi polycubes sub mapping is recognized as the most commonly used method for generating structured hexahedral mesh which has become a prior choice for mechanical simulation however volume decomposition process of sub mapping due to the diversity of entity structures still lacks support from stable algorithm moreover as a preprocessing step of sub mapping morphing process sometimes leads to unsatisfactory mesh quality in order to improve stability and meshing quality of sub mapping a digraph based structured hexahedral meshing method for coupled quasi polycubes is proposed in this paper the method avoids the processes of volume decomposition and morphing at first an initial manual decomposition is carried out the input model is decomposed into a number of sub entities with respect to which initial digraphs are built secondly virtual edges and vertices are constructed by means of mean value interpolation and then added into its corresponding digraph so as to build connections between subgraphs within one digraph thirdly face sheets are obtained by intersecting sub entities with one another vertices and edges of the face sheets are added into their corresponding sub entities digraphs to establish connections between digraphs of sub entities finally a linear system is constructed according to the solution of which the whole model is meshed experiments revealed in this paper demonstrate that the proposed method is applicable for all structured hexahedral mesh generation of coupled quasi polycubes

automatic hexahedral mesh generation using a new grid based method with geometry and mesh transformation a geometry and mesh transformation approach is proposed to overcome the traditional problem of poorly shaped elements at the boundary using the grid based method of mesh generation this is achieved by transforming the original geometric model to a topologically similar recognition model which conforms fully to the cartesian directions such a recognition model is constructed by tessellating the original model and then employing a fuzzy logic method to determine the normal directions of the faces a three dimensional field morphing algorithm is used to position the features of the recognition model such a recognition model is then meshed with hexahedral elements without any degeneracy using the new grid based algorithm the mesh of the recognition model is mapped back to the original geometric model by employing a transformation based on the laplacian isoparametric equation

dynamics of chaos order interface in coupled map lattices abstract we study a coupled map lattice model with two states a simple fixed point and spatio temporal chaos preparing properly initial conditions we investigate the dynamics of the interface between order and chaos in the one dimensional lattice regimes of irregular and regular front propagation behavior are observed and analyzed by introducing a local front map and a front lyapunov exponent corresponding to these different regimes of front propagation we can characterize different types of transitions from laminar state to chaos using comoving lyapunov exponents in the two dimensional lattice these types of front motion are related to regimes of roughening and flattening of the interface

dynamics control of chaotic systems by parametric destochastization it is shown that deterministic noise chaos appearing via destruction of the quasiperiodic motion may be easily suppressed by weak parametric perturbation of the system

rotational chaos in dissipative systems abstract an investigation is made into chaotic attractors arising from a quasiperiodic transition to chaos using a quantity called the rotation interval the rotation interval describes the short term rotation rates available to the attractor we present algorithms to calculate it given an appropriate map differential equation or time series we find that the rotation interval has a very robust parameter dependence its endpoints are almost always phase locked our numerical ideas are based on the theory of dissipative twist maps which is reviewed this theory is also used to prove a theorem about the non existence of certain strange attractors in nearly conservative systems finally an investigation is made into the relationship between the rotation interval and topological entropy and the breakup of invariant circles

the cumulant approach for investigating the noise influence on mode locking bifurcations the influence of noise on mode locking bifurcations is investigated for the circle map and for coupled logistic maps the technique based on the cumulant expansion is used for the bifurcation analysis of these systems it is shown that this cumulant analysis in gaussian approximation provides a suitable description of the influence of weak noise we find that the universal scaling properties for the circle map in the critical point for the golden mean sequence are the same as those obtained analytically using the path integral technique we find the same scaling behaviour in the case of weak multiplicative noise

the blocks and weights of finite special linear and unitary groups abstract this paper has two main parts first we give a classification of the l blocks of finite special linear and unitary groups sl n q in the non defining characteristic l 3 second we describe how the l weights of sl n q can be obtained from the l weights of gl n q when l gcd n q and verify the alperin weight conjecture for sl n q under the condition l gcd n q as a step to establish the alperin weight conjecture for all finite groups we prove the inductive blockwise alperin weight condition for any unipotent l block of sl n q if l gcd n q

return time entropies for a class of circle homeomorphisms poincare recurrence for a class of circle maps is used to study the properties of the corresponding invariant measures in the subcritical case when the map is a diffeomorphism the return time measure is smooth and in the critical case when the map is only a homeomorphism the measure is only continuous furthermore in the considered class of critical maps the behaviour of the return time entropy depends only on the tail in the continued fraction expansion of the rotation number

mode locking and arnold tongues in integrate and fire neural oscillators an analysis of mode locked solutions that may arise in periodically forced integrate and fire if neural oscillators is introduced based upon a firing map formulation of the dynamics a q p mode locked solution is identified with a spike train in which p firing events occur in a period q ensuremath delta where ensuremath delta is the forcing period a linear stability analysis of the map of firing times around such solutions allows the determination of the arnold tongue structure for regions in parameter space where stable solutions exist the analysis is verified against direct numerical simulations for both a sinusoidally forced if system and one in which a periodic sequence of spikes is used to induce a biologically realistic synaptic input current this approach is extended to the case of two synaptically coupled if oscillators showing that mode locked states can exist for some self consistently determined common period of repetitive firing numerical simulations show that such solutions have a bursting structure where regions of spiking activity are interspersed with quiescent periods before repeating the influence of the synaptic current upon the arnold tongue structure is explored in the regime of weak coupling

bifurcation and chaos in a periodically stimulated cardiac oscillator abstract periodic stimulation of an aggregate of spontaneously beating cultured cardiac cells displays phase locking period doubling bifurcations and aperiodic chaotic dynamics at different values of the stimulation parameters this behavior is analyzed by considering an experimentally determined one dimensional poincare or first return map a simplified version of the experimentally determined poincare map is proposed and several features of the bifurcations of this map are described

transition to topological chaos for circle maps abstract many biperiodic flows can be modelled by maps of a circle to itself for such maps the transition from zero to positive topological entropy can be achieved in several ways we describe all the possible routes for smooth circle maps and discuss the relevance of our results to the transition to chaos for two frequency systems

the w sequence for circle maps and misbehaved itineraries the w sequence an ordering of maximal itineraries for circle maps is constructed by means of the farey transformation and the gluing operation the similarity in the dynamical behaviour of the maps is explicitly described in terms of itineraries a class of badly ordered itineraries termed misbehaved is defined with the language of symbolic sequences a misbehaved itinerary is shown to imply a rotation interval

three coupled oscillators mode locking global bifurcations and toroidal chaos abstract many systems exhibit behaviour which can be described by three coupled oscillators provided the coupling is not too strong such systems can be modelled by maps of the two torus to itself in this paper we describe and explain those aspects of the bifurcation diagram for two parameter families of torus maps that involve change of mode locking type we introduce the concepts of partial and full mode locking for the coupled oscillators these notions correspond to the presence of one or two rational relations between the frequencies respectively numerical investigation of a particular family of torus maps reveals an intricate web of global bifurcations in order to explain the results we first show that we can approximate maps in the neighbourhood of a rational translation to arbitrary order by the time 1 map of a flow on the torus then we analyse those condimension 1 and 2 bifurcations for flows on the torus which change the set of frequency ratios we find a large variety of bifurcation diagrams in particular many involving homotopically non trivial saddle connections next we ask how the picture changes when the time 1 maps of a family of flows are perturbed to a general family of diffeomorphisms we find toroidal chaos in the neighbourhood of all these bifurcations meaning that there exist orbits which perform a pseudo random sequence of rotations in different directions around the torus the corresponding behaviour for the coupled oscillators is that the frequency ratios perform a random walk finally we show how all these ingredients can be put together to give global scenarios for bifurcation for families of torus maps which we believe to be of general applicability to physical systems with three weakly coupled modes of oscillation

explicit renormalisation in piecewise linear bimodal maps abstract we discuss 2 two parameter families of piecewise linear bimodal two hump maps the first example arises naturally in the study of bimodal maps any bimodal map is semi conjugate to a member of this family and topological entropy is preserved the second example is a symmetric subcase of a map derived from a simple pulse modulated feedback system in each case we define an explicit map of parameter space which governs the effect of renormalisation and use it to describe the non wandering set

density of hyperbolicity for classes of real transcendental entire functions and circle maps we prove density of hyperbolicity in spaces of i real transcendental entire functions bounded on the real line whose singular set is finite and real and ii transcendental self maps of the punctured plane which preserve the circle and whose singular set apart from zero and infinity is contained in the circle in particular we prove density of hyperbolicity in the famous arnol d family of circle maps and its generalizations and solve a number of other open problems for these functions including three conjectures by de melo salom ao and vargas we also prove density of real hyperbolicity for certain families as in i but without the boundedness condition our results apply in particular when the functions in question have only finitely many critical points and asymptotic singularities or when there are no asymptotic values and the degree of critical points is uniformly bounded

nonlinear dynamics chaos and complex cardiac arrhythmias periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one dimensional finite difference equations as stimulation parameters are varied a large number of different phase locked and chaotic rhythms is observed similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites simplified models are analysed which show some correspondence to clinical observations the normal adult human heart at rest usually beats at a rate of between 50 and 100 times per minute in many circumstances some of which are lifethreatening but most of which are not the normal rhythmicity is altered resulting in abnormal rhythms called cardiac arrhythmias the point of this paper is to show that a branch of mathematics called nonlinear dynamics may be useful in the analysis of physiological processes believed to underlie normal heart rate regulation and some cardiac arrhythmias the idea that mathematical analysis can play a role in understanding cardiac arrhythmias is not novel indeed in the 1920s it was demonstrated that as parameters in mathematical models for the heart were varied several different rhythms that resembled clinically observed arrhythmias could be generated mobitz 1924 van de pol van der mark 1928 in nonlinear mathematics these changes in the qualitative features of the rhythms that are observed as parameters vary are called bifurcations thus the problem of understanding cardiac arrhythmias in the human heart is identified with understanding the bifurcations and complex dynamics in mathematical models of the human heart one type of dynamic behaviour that is the object of intensive analysis in mathematics is chaos loosely chaos is defined as aperiodic dynamics in deterministic systems in which there is sensitive dependence to the initial conditions this means that although in principle one could determine precisely the future evolution of the system starting from some initial condition for chaotic dynamics any difference in the initial condition no matter how small will eventually lead to marked differences in the future evolution of the system although the existence of chaos was known to poincare and others since the end of the last century in the

bifurcations from an invariant circle for two parameter families of maps of the plane a computer assisted study we consider a two parameter family of maps of the plane to itself each map has a fixed point in the first quadrant and is a diffeomorphism in a neighborhood of this point for certain parameter values there is a hopf bifurcation to an invariant circle which is smooth for parameter values in a neighborhood of the bifurcation point however computer simulations show that the corresponding invariant set fails to be even topologically a circle for parameter values far from the bifurcation point this paper is an attempt to elucidate some of the mechanisms involved in this loss of smoothness and alteration of topological type

more on optimal stress points reduced integration element distortions and error estimation the presented work addresses the relationships between optimal sampling points reduced integration and geometric distortion with the objective of estimating errors in terms of those considerations isoparametric quadratic plane and solid elements are used as a vehicle for the study geometric distortion measures and evaluation conditions based on convergence requirements are first defined in terms of the polynomial orders of the geometry and applied strain using these the concept of optimal stress sampling already established for undistorted elements is extended to distorted geometry and shown to be effective over a range of geometries and strains errors in the strain displacement relationship and numerical integration of the strains are used to estimate the total response error and to rationalize the connection between optimal stress points and reduced integration enhanced convergence by extension to the representation of linear strains in elements with quadratic geometry is identified as the main advantage of reduced integration the applicability of the proposed and other distortion parameters to vetting of element geometry and error prediction is discussed

finite element euler computations in three dimensions an explicit finite element solution procedure for the three dimensional euler equations is presented the solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work several examples are included to illustrate the performance of the generator and solver an adaptive mesh regeneration procedure is used for the first time in three dimensions

mode locking in a periodically forced resonate and fire neuron model the resonate and fire rf model is a spiking neuron model which from a dynamical systems perspective is a piecewise smooth system impact oscillator we analyze the response of the rf neuron oscillator to periodic stimuli by expressing the firing events in terms of an implicit one dimensional time map based on such a firing map we describe mode locked solutions and their stability leading to the so called arnol d tongues the boundaries of these tongues correspond to either local bifurcations of the firing time map or grazing bifurcations of the discontinuity of the flow despite the fact that the periodically driven rf system shows periodic firing its behavior may become chaotic when the forcing frequency is near the resonant frequency we compare these results to numerical simulations of the model undergoing sinusoidal forcing furthermore upon varying a system parameter the rf system can be reduced to the integrate and fire system and in this case we show the consistency of the results on mode locked solutions

the boundary of chaos for interval mappings a goal in the study of dynamics on the interval is to understand the transition to positive topological entropy there is a conjecture from the 1980s that the only route to positive topological entropy is through a cascade of period doubling bifurcations we prove this conjecture in natural families of smooth interval maps and use it to study the structure of the boundary of mappings with positive entropy in particular we show that in families of mappings with a fixed number of critical points the boundary is locally connected and for analytic mappings that it is a cellular set

computational proof of the mackey formula for q 2 let g be a connected reductive group defined over a finite field with q elements we prove that the mackey formula for the lusztig induction and restriction holds in g whenever q 2 or g does not have a component of type e

unconstrained plastering hexahedral mesh generation via advancing front geometry decomposition the generation of all hexahedral finite element meshes has been an area of ongoing research for the past two decades and remains an open problem unconstrained plastering is a new method for generating all hexahedral finite element meshes on arbitrary volumetric geometries starting from an unmeshed volume boundary unconstrained plastering generates the interior mesh topology without the constraints of a pre defined boundary mesh using advancing fronts unconstrained plastering forms partially defined hexahedral dual sheets by decomposing the geometry into simple shapes each of which can be meshed with simple meshing primitives by breaking from the tradition of previous advancing front algorithms which start from pre meshed boundary surfaces unconstrained plastering demonstrates that for the tested geometries high quality boundary aligned orientation insensitive all hexahedral meshes can be generated automatically without pre meshing the boundary examples are given for meshes from both solid mechanics and geotechnical applications copyright 2009 john wiley sons ltd

existence d orbites quasi periodiques dans les attracteurs de birkhoff for each number between the lower and the upper rotation number of the birkhoff attractor of a dissipative monotone twist map there is a periodic or quasi periodic orbit with rotation number

dynamics near a periodically perturbed robust heteroclinic cycle abstract robust heteroclinic cycles rhcs arise naturally in collections of symmetric differential equations derived as dynamical models in many fields including fluid mechanics game theory and population dynamics in this paper we present a careful study of the complicated dynamics generated by small amplitude periodic perturbations of a stable robust heteroclinic cycle rhc we give a detailed derivation of the poincare map for trajectories near the rhc asymptotically correct in the limit of small amplitude perturbations this reduces the nonautonomous system in r 3 to a 2d map we identify three distinct dynamical regimes the distinctions between these regimes depend subtly on different distinguished limits of the two small parameters in the problem the first regime corresponds to the rhc being only weakly attracting here we show that the system is equivalent to a damped nonlinear pendulum with a constant torque in the second regime the periodically perturbed rhc is more strongly attracting and the system dynamics corresponds to that of a non invertible or invertible circle map in the third regime of yet stronger attraction the dynamics of the return map is chaotic and no longer reducible to a one dimensional map this third regime has been noted previously our analysis in this paper focusses on providing quantitative results in the first two regimes

onset of stochasticity for some one dimensional systems we study the appearance of stochastic dynamics in two situations 1 i for one parameter families of maps of the interval f undergoing an infinite sequence of period doubling bifurcations we consider 0 0 e beyond feigenbaum s parameter value 0 2 ii for a two parameter family of circle maps fb x x b2pisin2 x we consider b 1 1 e 0 1 in both cases we estimate the relative measure of parameter values corresponding to stochastic behavior

finite element mesh control by integer programming a novel technique is presented for the control of mapped quadrilateral and hexahedral meshes generated inside a collection of connected subregions target division numbers on the subregion edges are given as input by allowing these numbers to vary meshes can be found which satisfy both the subregion constraints imposed by the mesh patterns being employed and the compatibility constraints on edges shared by two or more adjacent subregions among all such feasible solutions the optimal one is obtained by minimizing the changes to the division numbers using an integer programming technique

renormalization of c 0 bimodal maps abstract we consider c 0 bimodal maps of the interval we show how topological renormalization may be defined for maps with both zero and positive entropy this has been done before but for the case of positive entropy we use a theorem of milnor and thurston to give a new highly intuitive definition which does not use kneading theory and avoids the technical problems of previous approaches

on jordan decomposition of characters for su n q abstract as shown by bonnafe a step in proving a jordan decomposition of characters of finite special linear groups is the parametrization of unipotent characters of centralizers of semi simple elements in projective linear groups we show the same kind of result in the case of finite special unitary groups the proof leads to a mild adaptation of bonnafe s methods expounded in b99 the outcome is a jordan decomposition of characters compatible with lusztig s twisted induction

automatic generation of multiblock decompositions of surfaces summary multiblock structured meshes have significant advantages over fully unstructured meshes in numerical simulation but automatically generating these meshes is considerably more difficult a method is described herein for automatically generating high quality multiblock decompositions of surfaces with boundaries controllability and flexibility are useful capabilities of the method additional alignment constraints for forcing the appearance of particular features in the decomposition can be easily handled also adjustments are made according to input metric tensor fields that describe target element size properties the general solution strategy is based around using a four way symmetry vector field called a cross field to describe the local mesh orientation on a triangulation of the surface initialisation is performed by propagating the boundary alignment constraints to the interior in a fast marching method this is similar in a way to an advancing front or paving method but much more straightforward and flexible because mesh connectivity does not have to be managed in the cross field multiblock decompositions are generated by tracing the separatrices of the cross field to partition the surface into quadrilateral blocks with square corners the final task of meshing the decomposition requires solving an integer programming problem for block division numbers copyright 2015 john wiley sons ltd

generalization of voronoi diagrams in the plane in this paper we study the voronoi diagram for a set of n line segments and circles in the euclidean plane the diagram is a generalization of the voronoi diagram for a set of points in the plane and has applications in wire layout facility location clustering and contouring problems we present an o n log n 2 algorithm for constructing the diagram it is an improvement of a previous known result which takes o nc sqrt log n time the algorithm described in this paper is also shown to be applicable under a more general metric if certain conditions are satisfied

on the discrete core of quadrilateral mesh refinement we present a new approach to quadrilateral mesh refinement which reduces the problem to its structural core the resulting problem formulation belongs to a class of discrete problems network flow problems which has been thoroughly investigated and is well understood the network flow model is flexible enough to allow the simultaneous incorporation of various aspects such as the control of angles and aspect ratios local density control and templates meshing primitives for the internal refinement of mesh elements we show that many different variants of the general quadrilateral mesh refinement problem are covered in particular we present a novel strategy which provably finds a conformal refinement unless there is none copyright 1999 john wiley sons ltd