the weak lefschetz property of equigenerated monomial ideals abstract we determine a sharp lower bound for the hilbert function in degree d of a monomial algebra failing the weak lefschetz property over a polynomial ring with n variables and generated in degree d for any d 2 and n 3 we consider artinian ideals in the polynomial ring with n variables generated by homogeneous polynomials of degree d invariant under an action of the cyclic group z d z for any n 3 and any d 2 we give a complete classification of such ideals in terms of the weak lefschetz property depending on the action

invariant measures exist under a summability condition for unimodal maps for unimodal maps with negative schwarzian derivative a sufficient condition for the existence of an invariant measure absolutely continuous with respect to lebesgue measure is given namely the derivatives of the iterations of the map in the unique critical value must be so large that the sum of some root of the inverses is finite

free resolutions of artinian compressed algebras abstract we construct free resolutions of compressed therefore generic artinian graded algebra quotients of polynomial rings and give a method to reduce them to a minimal resolutions this yields results on the form of the resolution and the degrees of the forms in the matrices of the differentials but not precise betti numbers in addition we discuss how this construction is related to a conjecture of boij last we treat the noncompressed case

hyperbolicity and invariant measures for general c 2 interval maps satisfying the misiurewicz condition in this paper we will show that piecewise c2 mappings on 0 1 or s1 satisfying the so called misiurewicz conditions are globally expanding in the sense defined below and have absolute continuous invariant probability measures of positive entropy we do not need assumptions on the schwarzian derivative of these maps instead we need the conditions that is piecewise c2 that all critical points of are non flat and that has no periodic attractors our proof gives an algorithm to verify this last condition our result implies the result of misiurewicz in mi where only maps with negative schwarzian derivatives are considered moreover as a byproduct the present paper implies and simplifies the proof of the results of mane in ma who considers general c2 maps without conditions on the schwarzian derivative and restricts attention to points whose forward orbit stay away from the critical points one of the main complications will be that in this paper we want to prove the existence of invariant measures and therefore have to consider points whose iterations come arbitrarily close to critical points misiurewicz deals with this problem using an assumption on the schwarzian derivative of the map this assumption implies very good control of the non linearity of even for high n in order to deal with this non linearity without an assumption on the schwarzian derivative we use the tools of m s it will turn out that the estimates we obtain are so precise that the existence of invariant measures can be proved in a very simple way in some sense much simpler than in mi the existence of these invariant measures under such general conditions was already conjectured a decade ago

on the use of reverse brownian motion to accelerate hybrid simulations multiscale and multiphysics simulations are two rapidly developing fields of scientific computing efficient coupling of continuum deterministic or stochastic constitutive solvers with their discrete stochastic particle based counterparts is a common challenge in both kinds of simulations we focus on interfacial tightly coupled simulations of diffusion that combine continuum and particle based solvers the latter employs the reverse brownian motion rbm a monte carlo approach that allows one to enforce inhomogeneous dirichlet neumann or robin boundary conditions and is trivially parallelizable we discuss numerical approaches for improving the accuracy of rbm in the presence of inhomogeneous neumann boundary conditions and alternative strategies for coupling the rbm solver with its continuum counterpart numerical experiments are used to investigate the convergence stability and computational efficiency of the proposed hybrid algorithm

adaptive mesh and algorithm refinement using direct simulation monte carlo adaptive mesh and algorithm refinement amar embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement amr hierarchy the coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of amr direct simulation monte carlo dsmc is used as the particle algorithm embedded within a godunov type compressible navier stokes solver several examples are presented and compared with purely continuum calculations

on the weak lefschetz property for artinian gorenstein algebras of codimension three abstract we study the problem of whether an arbitrary codimension three graded artinian gorenstein algebra has the weak lefschetz property we reduce this problem to checking whether it holds for all compressed gorenstein algebras of odd socle degree in the first open case namely hilbert function 1 3 6 6 3 1 we give a complete answer in every characteristic by translating the problem to one of studying geometric aspects of certain morphisms from p 2 to p 3 and hesse configurations in p 2

rigidity of c 2 infinitely renormalizable unimodal maps given c 2 infinitely renormalizable unimodal maps f and g with a quadratic critical point and the same bounded combinatorial type we prove that they are c 1 conjugate along the closure of the corresponding forward orbits of the critical points for some 0

a phase transition for circle maps and cherry flows we study c2 weakly order preserving circle maps with a flat interval the main result of the paper is about a sharp transition from degenerate geometry to bounded geometry depending on the degree of the singularities at the boundary of the flat interval we prove that the non wandering set has zero hausdorff dimension in the case of degenerate geometry and it has hausdorff dimension strictly greater than zero in the case of bounded geometry our results about circle maps allow to establish a sharp phase transition in the dynamics of cherry flows

rational rotation numbers for maps of the circle we consider families of maps of the circle of degree 1 which are homeomorphisms but not diffeomorphisms that is maps like x to x t frac c 2 pi sin 2 pi x bmod 1 withc 1 we prove that the set of parameter values corresponding to irrational rotation numbers has lebesgue measure 0 in other words the intervals on which frequency locking occurs fill up the set of full measure

the weak lefschetz property of gorenstein algebras of codimension three associated to the apery sets abstract it has been conjectured that all graded artinian gorenstein algebras of codimension three have the weak lefschetz property over a field of characteristic zero in this paper we study the weak lefschetz property of associated graded algebras a of the apery set of m pure symmetric numerical semigroups generated by four natural numbers in 2010 bryant proved that these algebras are graded artinian gorenstein algebras of codimension three in a recent article guerrieri showed that if a is not a complete intersection then a is of form a r i with r k x y z and i x a y b x b z z c x a b y b y b z c where 1 b 1 max 1 b a 1 min b 1 c 1 and a c 2 we prove that a has the weak lefschetz property in the following cases max 1 b a c 1 b 1 and a b c 2 2 a 2 b c and a b c 1 b 1 one of a b c is at most five

invariant measures for cherry flows we investigate the invariant probability measures for cherry flows i e flows on the two torus which have a saddle a source and no other fixed points closed orbits or homoclinic orbits in the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the dirac measures at the two fixed points and the dirac measure at the saddle is the physical measure in the other case we prove that there exists also an invariant probability measure supported on the quasi minimal set we discuss some situations when this other invariant measure is the physical measure and conjecture that this is always the case the main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow and the study of the close returns near the saddle

numerical integration of the fluctuating hydrodynamic equations an approach to numerically integrate the landau lifshitz fluctuating hydrodynamic equations is outlined the method is applied to one dimensional systems obeying the nonlinear fourier equation and the full hydrodynamic equations for a dilute gas static spatial correlation functions are obtained from computer generated sample trajectories time series they are found to show the emergence of long range behavior whenever a temperature gradient is applied the results are in very good agreement with those obtained from solving the correlation equations directly

the fibonacci unimodal map the fibonacci recurrence of the critical orbit appeared in the work of branner and hubbard on complex cubic polynomials bh 12 and in yoccoz s work yl y2 on quadratic ones as the worst pattern of recurrence on the other hand a real quadratic fibonacci map was suggested by hofbauer and keller hk as a possible candidate for a map having a wild attractor that is a set a which is the w limit set for lebesgue almost every orbit but is strictly smaller than the w limit set for a generic orbit the w limit set of the critical orbit in hk possesses all known topological properties of wild attractors compare bl2 in fact we will see below that the quadratic fibonacci map does not have a wild attractor however the corresponding question for a map with a degenerate critical point remains open actually the first indication of the fibonacci map appeared in the numerical work of tsuda t related to the belousova zhabotinskii reaction and also in numerical work of shibayama sh more precisely they studied the sequence of fibonacci bifurcations creating the fibonacci map this paper will study topological geometrical and measure theoretical properties of the real fibonacci map our goal was to figure out if this type of recurrence really gives any pathological examples and to compare it with the infinitely renormalizable patterns of recurrence studied by sullivan s it turns out that the situation can be understood completely and is of quite regular nature in particular any fibonacci map with negative schwarzian and nondegenerate critical point has an absolutely continuous invariant measure so we deal with a regular type of chaotic dynamics it turns out also that geometrical properties of the closure of the critical orbit are quite different from those of the feigenbaum map its hausdorff dimension is equal to zero and its geometry is not rigid but depends on one parameter branner and hubbard introduce the concept of a tableau in order to describe recurrence of critical orbits their fibonacci tableau is a basic example which corresponds to one particularly close and regular pattern of recurrence if a complex quadratic map z 1 z2 c realizes this fibonacci tableau then the

algorithm refinement for the stochastic burgers equation in this paper we develop an algorithm refinement ar scheme for an excluded random walk model whose mean field behavior is given by the viscous burgers equation ar hybrids use the adaptive mesh refinement framework to model a system using a molecular algorithm where desired while allowing a computationally faster continuum representation to be used in the remainder of the domain the focus in this paper is the role of fluctuations on the dynamics in particular we demonstrate that it is necessary to include a stochastic forcing term in burgers equation to accurately capture the correct behavior of the system the conclusion we draw from this study is that the fidelity of multiscale methods that couple disparate algorithms depends on the consistent modeling of fluctuations in each algorithm and on a coupling such as algorithm refinement that preserves this consistency

critical circle maps near bifurcation we estimate harmonic scalings in the parameter space of a one parameter family of critical circle maps these estimates lead to the conclusion that the hausdorff dimension of the complement of the frequency locking set is less than 1 but not less than 1 3 moreover the rotation number is a holder continuous function of the parameter

fatou and julia sets for entire mappings in bbb c k the fatou set is just made of basins of attraction correspondingto attracting cycles and that hyperbolic periodic cycles are dense in the julia set similar results are obtained in fs3 fs4 for other classes of mappings seetheorems 2 9 and 2 10 below in bu buzzard proved a version of the kupka smale theorem for

differentiable circle maps with a flat interval we study weakly order preserving circle maps with a flat interval which are differentiable even on the boundary of the flat interval we obtain estimates on the lebesgue measure and the hausdorff dimension of the non wandering set also a sharp transition is found from degenerate geometry to bounded geometry depending on the degree of the singularities at the boundary of the flat interval

thin algebras of embedding dimension three let r r0 r1 r2 be a finitely generated commutative graded k algebra with hilbert series hr n 0dimk rn n suppose we require that r have a presentation as r k x1 xg 1 r where g and r and the degrees d1 dr of the homogeneous polynomials 1 r are specified in advance no one knows precisely which hubert series such an r may have a lower bound is the coefficient wise inequality hr 1 g i 1r 1 di absolute value symbols denoting the initial non negative segment of a power series can this lower bound always be attained this deceptively simple sounding question has been answered affirmatively only when g 2 r froberg report no 37 department of mathematics university of stockholm stockholm sweden 1982 a iarrobino memoir no 188 amer math soc providence r i 1977 when r g and when r g 1 and char k 0 a iarrobino compressed algebras trans amer math soc 285 1984 337 378 this paper considers the case g 3 settling it affirmatively whenever k is an infinite field

reduced basis anova methods for partial differential equations with high dimensional random inputs in this paper we present a reduced basis anova approach for partial deferential equations pdes with random inputs the anova method combined with stochastic collocation methods provides model reduction in high dimensional parameter space through decomposing high dimensional inputs into unions of low dimensional inputs in this work to further reduce the computational cost we investigate spatial low rank structures in the anova collocation method and develop efficient spatial model reduction techniques using hierarchically generated reduced bases we present a general mathematical framework of the methodology validate its accuracy and demonstrate its efficiency with numerical experiments

julia fatou sullivan theory for real one dimensional dynamics our aim is to show that the julia fatou sullivan structure theory for the dynamics of rational maps is also valid for smooth endomorphisms of the circle and of the interval under extremely mild smoothness and non flatness conditions in order to stress the similarity between real and complex one dimensional dynamics let us recall the main results from the fatou julia sullivan theory if f is a rational map then there is a dynamical decomposition of the riemann sphere into the disjoint union of two totally invariant i e both forward and backward invariant sets j f f f here f f is the domain of normality of the family of iterates of f and is called the fatou set its complement which is called the julia set off is a compact set which contains all the complications of the dynamics off the connected components of the open set f f are mapped onto each other by f hence the orbit of a component of f f is the union of some components of f f julia proved in the beginning of the century that if a component of f f is periodic and contains an attracting periodic point then the orbit of this component must contain a critical point sullivan in the remarkable paper su showed via quasi conformal deformations that the components are eventually periodic and fall into finitely many orbits let n be either the circle s j or a compact interval of the real line and f n n be a smooth endomorphism a critical point of f is a point where the derivative vanishes a critical point is non flat if some higher derivative is non zero a critical point is an inflection point if it has a neighbourhood where f is monotone otherwise it is called a turning point assume f is not a homeomorphism i f f is a homeomorphism then these maps correspond to degree 1 rational maps of the riemann sphere and the situation is

numerical methods for the stochastic landau lifshitz navier stokes equations the landau lifshitz navier stokes llns equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes this paper examines explicit eulerian discretizations of the full llns equations several computational fluid dynamics approaches are considered including maccormack s two step lax wendroff scheme and the piecewise parabolic method and are found to give good results for the variance of momentum fluctuations however neither of these schemes accurately reproduces the fluctuations in energy or density we introduce a conservative centered scheme with a third order runge kutta temporal integrator that does accurately produce fluctuations in density energy and momentum a variety of numerical tests including the random walk of a standing shock wave are considered and results from the stochastic llns solver are compared with theory when available and with molecular simulations using a direct simulation monte carlo algorithm

a domain decomposition approach for uncertainty analysis this paper proposes a decomposition approach for uncertainty analysis of systems governed by partial differential equations pdes the system is split into local components using domain decomposition our domain decomposed uncertainty quantification dduq approach performs uncertainty analysis independently on each local component in an offline phase and then assembles global uncertainty analysis results using precomputed local information in an online phase at the heart of the dduq approach is importance sampling which weights the precomputed local pde solutions appropriately so as to satisfy the domain decomposition coupling conditions to avoid global pde solves in the online phase a proper orthogonal decomposition reduced model provides an efficient approximate representation of the coupling functions

algorithm refinement for stochastic partial differential equations i linear diffusion a hybrid particle continuum algorithm is formulated for fickian diffusion in the fluctuating hydrodynamic limit the particles are taken as independent random walkers the fluctuating diffusion equation is solved by finite differences with deterministic and white noise fluxes at the interface between the particle and continuum computations the coupling is by flux matching giving exact mass conservation this methodology is an extension of adaptive mesh and algorithm refinement to stochastic partial differential equations results from a variety of numerical experiments are presented for both steady and time dependent scenarios in all cases the mean and variance of density are captured correctly by the stochastic hybrid algorithm for a nonstochastic version i e using only deterministic continuum fluxes the mean density is correct but the variance is reduced except in particle regions away from the interface extensions of the methodology to fluid mechanics applications are discussed

absolutely continuous invariant measures for one parameter families of one dimensional maps given a one parameter familyf x of maps of the interval 0 1 we consider the set of parameter values for whichf has an invariant measure absolutely continuous with respect to lebesgue measure we show that this set has positive measure for two classes of maps i f x f x where 0 4 andf x is a functionc3 near the quadratic mapx 1 x and ii f x f x mod 1 wheref isc3 f 0 f 1 0 andf has a unique nondegenerate critical point in 0 1

quadratic maps without asymptotic measure an interval map is said to have an asymptotic measure if the time averages of the iterates of lebesgue measure converge weakly we construct quadratic maps which have no asymptotic measure we also find examples of quadratic maps which have an asymptotic measure with very unexpected properties e g a map with the point mass on an unstable fix point as asymptotic measure the key to our construction is a new characterization of kneading sequences

a generalized lower bound theorem for balanced manifolds a simplicial complex of dimension d 1 is said to be balanced if its graph is d colorable juhnke kubitzke and murai proved an analogue of the generalized lower bound theorem for balanced simplicial polytopes we establish a generalization of their result to balanced triangulations of closed homology manifolds and balanced triangulations of orientable homology manifolds with boundary under an additional assumption that all proper links of these triangulations have the weak lefschetz property as a corollary we show that if delta is an arbitrary balanced triangulation of any closed homology manifold of dimension d 1 ge 3 then 2h 2 delta d 1 h 1 delta ge 4 d atopwithdelims 2 tilde beta 1 delta tilde beta 0 delta thus verifying a conjecture by klee and novik to prove these results we develop the theory of flag h vectors

analyticity properties of the feigenbaum function analyticity properties of the feigenbaum function a solution ofg x 1g g x withg 0 1 g 0 0 g 0 0 are investigated by studying its inverse function which turns out to be herglotz or anti herglotz on all its sheets it is found thatg is analytic and uniform in a domain with a natural boundary

scalings in circle maps i letf be a flat spot circle map with irrational rotation number located at the edges of the flat spot are non flat critical points s x axv v 1 first we define scalings associated with the closest returns of the orbit of the critical point under the assumption that these scalings go to zero we prove that the derivative of long iterates of the critical value can be expressed in the scalings the asymptotic behavior of the derivatives and the scalings can then be calculated we concentrate on the cases for which one can prove the above assumption in particular let one of the singularities be linear these maps arise for example as the lower bound of the non decreasing truncations of non invertible bimodal circle maps it follows that the derivatives grow at a sub exponential rate

looking out for stable syzygy bundles abstract we study slope stability properties of syzygy bundles on a projective space p n given by ideal generators of a homogeneous primary ideal in particular we give a combinatorial criterion for a monomial ideal to have a semistable syzygy bundle restriction theorems for semistable bundles yield the same stability results on the generic complete intersection curve from this we deduce a numerical formula for the tight closure of an ideal generated by monomials or by generic homogeneous elements in a generic two dimensional complete intersection ring

monomial ideals almost complete intersections and the weak lefschetz property many algebras are expected to have the weak lefschetz property though this is often very difficult to establish we illustrate the subtlety of the problem by studying monomial and some closely related ideals our results exemplify the intriguing dependence of the property on the characteristic of the ground field and on arithmetic properties of the exponent vectors of the monomials

nonexistence of wandering domains for strongly dissipative infinitely renormalizable henon maps at the boundary of chaos this article generalizes the nonexistence of wandering domains from unimodal maps to infinitely period doubling renormalizable henon like maps in the strongly dissipative area contracting regime this solves an open problem proposed by van strien discrete contin dyn syst 27 2 557 588 2010 and lyubich and martens invent math 186 1 115 189 2011 we partition the phase space of a henon like map into two regions the good region and the bad region the good region is where the method of proof for unimodal maps applies to henon like maps while the bad region is where serious difficulties occur these difficulties are resolved by the two row lemma an inequality that relates the contraction of areas to the contraction of bad regions after analyzing the competition of the two types of contraction we show that the case of bad regions happens at most finitely many times and complete the proof as an application the theorem enriches our understanding of the topological structure of the heteroclinic web the union of the stable manifolds of periodic orbits forms a dense set in the domain

on higher hessians and the lefschetz properties abstract we deal with a generalization of a theorem of p gordan and m noether on hypersurfaces with vanishing first hessian we prove that for any given n 3 d 3 and 2 k d 2 there are irreducible hypersurfaces x v f p n of degree deg f d not cones and such that their hessian of order k hess f k vanishes identically the vanishing of higher hessians is closely related with the strong or weak lefschetz property for standard graded artinian gorenstein algebra as pointed out first in 31 and later in 24 as an application we construct for each pair n d 3 3 3 4 standard graded artinian gorenstein algebras a of codimension n 1 4 and with socle degree d 3 which do not satisfy the strong lefschetz property failing at an arbitrary step k with 2 k d 2 we also prove that for each pair n d n 3 and d 3 except 3 3 3 4 3 6 and 4 4 there are standard graded artinian gorenstein algebras of codimension n 1 socle degree d with unimodal hilbert vectors and which do not satisfy the weak lefschetz property

positive lyapunov exponents in families of one dimensional dynamical systems we give a generalization of jakobson s theorem ja and a precise estimate for the density of parameters corresponding to systems with absolutely continuous invariant measures

one dimensional dynamics the schwarzian derivative and beyond most of the important results in the study of the dynamics of smooth interval maps 0 1 0 1 assume the condition that s f 0 where s f is the schwarzian derivative of

togliatti systems and galois coverings abstract we study the homogeneous artinian ideals of the polynomial ring k x y z generated by the homogeneous polynomials of degree d which are invariant under an action of the cyclic group z d z for any d 3 we prove that they are all monomial togliatti systems and that they are minimal if the action is defined by a diagonal matrix having on the diagonal 1 e e a where e is a primitive d th root of the unity we get a complete description when d is prime or a power of a prime we also establish the relation of these systems with linear ceva configurations

hyperbolicity sinks and measure in one dimensional dynamics letf be ac2 map of the circle or the interval and let f denote the complement of the basins of attraction of the attracting periodic orbits we prove that f is a hyperbolic expanding set if and obviously only if every periodic point is hyperbolic and f doesn t contain the critical point this is the real one dimensional version of fatou s hyperbolicity criteria for holomorphic endomorphisms of the riemann sphere we also explore other applications of the techniques used for the result above proving for instance that for everyc2 immersionf of the circle i e a map of the circle onto itself without critical points either its julia set has measure zero or it is the whole circle and thenf is ergodic i e positively invariant borel sets have zero or full measure

the weak and strong lefschetz properties for artinian k algebras abstract let a i 0ai be a standard graded artinian k algebra where chark 0 then a has the weak lefschetz property if there is an element l of degree 1 such that the multiplication l a i a i 1 has maximal rank for every i and a has the strong lefschetz property if l d a i a i d has maximal rank for every i and d the main results obtained in this paper are the following 1 every height three complete intersection has the weak lefschetz property our method surprisingly uses rank two vector bundles on p 2 and the grauert mulich theorem 2 we give a complete characterization including a concrete construction of the hilbert functions that can occur for k algebras with the weak or strong lefschetz property and the characterization is the same one 3 we give a sharp bound on the graded betti numbers achieved by our construction of artinian k algebras with the weak or strong lefschetz property and fixed hilbert function this bound is again the same for both properties some hilbert functions in fact force the algebra to have the maximal betti numbers 4 every artinian ideal in k x y possesses the strong lefschetz property this is false in higher codimension

the lefschetz properties of monomial complete intersections in positive characteristic abstract stanley proved that in characteristic zero all artinian monomial complete intersections have the strong lefschetz property we provide a positive characteristic complement to stanley s result in the case of artinian monomial complete intersections generated by monomials all of the same degree and also for arbitrary artinian monomial complete intersections in characteristic two to establish these results we first prove an a priori lower bound on the characteristics that guarantee the lefschetz properties we then use a variety of techniques to complete the classifications

the non lefschetz locus abstract we study the weak lefschetz property of artinian gorenstein algebras and in particular of artinian complete intersections in codimension four and higher it is an open problem whether all complete intersections have the weak lefschetz property for a given artinian gorenstein algebra a we ask what linear forms are lefschetz elements for this particular algebra i e which linear forms l give maximal rank for all the multiplication maps l a i a i 1 this is a zariski open set and its complement is the non lefschetz locus for monomial complete intersections we completely describe the non lefschetz locus for general complete intersections of codimension three and four we prove that the non lefschetz locus has the expected codimension which in particular means that it is empty in a large family of examples for general gorenstein algebras of codimension three with a given hilbert function we prove that the non lefschetz locus has the expected codimension if the first difference of the hilbert function is of decreasing type for completeness we also give a full description of the non lefschetz locus for artinian algebras of codimension two

algorithm refinement for stochastic partial differential equations ii correlated systems we analyze a hybrid particle continuum algorithm for a hydrodynamic system with long ranged correlations specifically we consider the so called train model for viscous transport in gases which is based on a generalization of the random walk process for the diffusion of momentum this discrete model is coupled with its continuous counterpart given by a pair of stochastic partial differential equations at the interface between the particle and continuum computations the coupling is by flux matching giving exact mass and momentum conservation this methodology is an extension of our stochastic algorithm refinement ar hybrid for simple diffusion f alexander a garcia d tartakovsky algorithm refinement for stochastic partial differential equations i linear diffusion j comput phys 182 2002 47 66 results from a variety of numerical experiments are presented for steady state scenarios in all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm for a non stochastic version i e using only deterministic continuum fluxes the long range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude

a structure theorem in one dimensional dynamics on considere la classe 7b a des applications c f 0 1 0 1 telles que f 0 f 1 0 et f a un unique point critique c 0 1 si le point critique de f 7b a est non plat alors f n a pas d intervalle errant

absolutely continuous invariant measures forc2 unimodal maps satisfying the collet eckmann conditions in this paper we show that unimodal mappingsf 0 1 0 1 have absolutely continuous measures of positive entropy if these maps arec2 and satisfy the so called collet eckmann conditions no conditions on the schwarzian derivative off are assumed

on the structure of monomial complete intersections in positive characteristic abstract in this paper we study the lefschetz properties of monomial complete intersections in positive characteristic we give a complete classification of the strong lefschetz property when the number of variables is at least three which proves a conjecture by cook ii we also extend earlier results on the weak lefschetz property by dropping the assumption on the residue field being infinite and by giving new sufficient criteria

the weak lefschetz property for monomial ideals of small type abstract in this work a combinatorial approach towards the weak lefschetz property is developed that relates this property to enumerations of signed perfect matchings as well as to enumerations of signed families of non intersecting lattice paths in certain triangular regions this connection is used to study artinian quotients by monomial ideals of a three dimensional polynomial ring extending a main result in the recent memoir 1 we completely classify the quotients of type two that have the weak lefschetz property in characteristic zero we also derive results in positive characteristic for quotients whose type is at most two

topological conditions for the existence of absorbing cantor sets this paper deals with strange attractors of s unimodal rnaps f it generalizes earlier results in the sense that very general topological conditions are given that either i guarantee the existence of an absorbing cantor set provided t he critical point of f is sufficiently degenerate or ii prohibit the existence of an absorbing cantor set altogether as a by product we obtain very weak topological conditions that imply the existence of an absolutely continuous invariant probability measure for f

a combined continuum dsmc technique for multiscale analysis of microfluidic filters a multiscale method that combines continuum fluid models with the direct simulation monte carlo dsmc method is presented the continuum regions are treated by stokes equations and a scattered point based finite cloud method is employed to solve the stokes equations the continuum and dsmc regions are combined by an overlapped schwarz alternating method with dirichlet dirichlet type boundary conditions a scattered point interpolation scheme is developed to interpolate the solution between subdomains the convergence characteristics of the multiscale approach are investigated in detail specifically the dependence of convergence on the overlap size the dsmc noise and the number of time steps employed in the dsmc algorithm are studied while the convergence depends weakly on the dsmc noise and the overlap size the number of dsmc time steps simulated in each coupling iteration should be selected so that the total time steps simulated until convergence of the coupled process is close to the time constant of the dsmc subsystem steady state analysis of microfluidic filters is studied in detail using the multiscale approach the multiscale approach is also applied for the simulation of a membrane with an array of microfluidic filters and a dual stage microfluidic device with an array of microfluidic filters for particle trapping and sorting

hyperbolicity properties of multi modal collet eckmann maps without schwarzian derivative assumptions in this paper we study the dynamical properties of general c2 maps f 0 1 0 1 with quadratic critical points and not necessarily unimodal we will show that if such maps satisfy the well known collet eckmann conditions then one has a hyperbolicity on the set of periodic points b nonexistence of wandering intervals c sensitivity on initial conditions and d exponential decay of branches intervals of monotonicity of fn as n oo for these results we will not make any assumptions on the schwarzian derivative f we will also give an estimate of the return time of points that start near critical points

fractal fourier spectra of cherry flows flows on the 2 torus with points of equilibrium are considered numerical observations suggest that for the case of trajectories with irrational rotation numbers power spectra are singular continuous dynamics is adequately represented by a symbolic sequence built from four symbols with the help of a substitution rule this rule effectively takes into account the slowing down of the motion during passages near the saddle point and the superexponential scaling of returns onto a secant line

renormalization in the henon family ii the heteroclinic web we study highly dissipative henon maps f c b x y mapsto c x 2 by x with zero entropy they form a region in the parameter plane bounded on the left by the curve w of infinitely renormalizable maps we prove that morse smale maps are dense in but there exist infinitely many different topological types of such maps even away from w we also prove that in the infinitely renormalizable case the average jacobian bf on the attracting cantor set mathcal o f is a topological invariant these results come from the analysis of the heteroclinic web of the saddle periodic points based on the renormalization theory along these lines we show that the unstable manifolds of the periodic points form a lamination outside mathcal o f if and only if there are no heteroclinic tangencies