on stabilized finite element methods for the reissner mindlin plate model stabilized finite element formulation for the reissner mindlin plate model is considered physical interpretation for the stabilization procedure for low order elements is established explicit interpolation functions for linear and bilinear stabilized mitc elements are derived some numerical examples including buckling and frequency analyses are presented copyright 2007 john wiley sons ltd

existence of dynamical hull functions with two variables for the ac driven frenkel kontorova model abstract in this paper we are concerned with the dynamics of incommensurate structures in the overdamped limit case of the frenkel kontorova model with periodic driving force we show in the infinite dimensional phase space there exists an ordered circle on which both the poincare map and the space shift map induce orientation preserving circle homeomorphisms with rotation numbers and respectively the latter characterizing the mean spacing of particles furthermore we prove that the average velocity for the particle chain with irrational exists and t where t denotes the period of the driving force and it is continuous and nondecreasing with respect to f the average of the external driving force if the shift map on the invariant ordered circle is ergodic we demonstrate the existence of two variable dynamical hull functions and that there are no mode locking behaviors

the discrete frenkel kontorova model and its extensions i exact results for the ground states abstract we present a rigorous study of the classical ground states under boundary conditions of a class of one dimensional models generalizing the discrete frenkel kontorova model the extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic quasi periodic and chaotic orbits for all boundary conditions we select among all the extremum solutions of the energy of the model those which correspond to the ground states of the infinite system we prove that these ground states are either periodic commensurate or quasi periodic incommensurate but are never chaotic we also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions the topological structure of the whole set of ground states is described in details in addition to physical applications consequences for twist map homeomorphisms are mentioned part ii s aubry p y ledaeron and g andre will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map

optimal solutions of linear control systems with nonperiodic convex integrands in this work we study the existence and asymptotic behaviour of overtaking optimal trajectories for a linear system with a nonperiodic convex cost function we extend the results obtained by leizarowitz leizarowitz a 1986 tracking nonperiodic trajectories with the overtaking criterion appl math opt 14 155 171 for a problem of tracking a prescribed nonperiodic trajectory with a quadratic cost function and establish the existence and uniqueness of optimal trajectories on an infinite horizon the asymptotic dynamics of finite time optimizers is examined

morse theory on spaces of braids and lagrangian dynamics in the first half of the paper we construct a morse type theory on certain spaces of braid diagrams we define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows defined on discretized braid spaces parabolic flows a type of one dimensional lattice dynamics evolve singular braid diagrams in such a way as to decrease their topological complexity algebraic lengths decrease monotonically this topological invariant is derived from a morse conley homotopy index in the second half of the paper we apply this technology to second order lagrangians via a discrete formulation of the variational problem this culminates in a very general forcing theorem for the existence of infinitely many braid classes of closed orbits

turnpike results for discrete time optimal control systems arising in economic dynamics abstract in this work we study the structure of approximate solutions of an autonomous discrete time control system with a compact metric space of states x this control system is described by a bounded upper semicontinuous function v x x r 1 which determines an optimality criterion and by a nonempty closed set x x which determines a class of admissible trajectories programs we are interested in turnpike properties of the approximate solutions which are independent of the length of the interval for all sufficiently large intervals for when x is a compact convex subset of a finite dimensional euclidean space the set is convex and the function v is strictly concave we obtain a full description of the structure of approximate solutions

structure of approximate solutions of discrete time optimal control bolza problems on large intervals abstract in this paper we study the structure of approximate solutions of an autonomous discrete time optimal control system with a compact metric space of states these optimal control systems are discrete time analogs of bolza problems in the calculus of variations we obtain the full description of approximate solutions of these problems on large intervals this description shows that on large intervals the approximate solutions are determined mainly by our optimality criterion and are essentially independent of the choice of time intervals and data

h sub spl infin differential riccati equations convergence properties and finite escape phenomena the paper studies the transient and asymptotic behavior of the solution of the sign indefinite differential riccati equation dre arising in finite horizon h sub spl infin filtering and control problems differently from the sign definite h sub spl infin dre the solution of the h sub spl infin dre can have finite escape times even for nonnegative initial conditions sufficient and necessary conditions for boundedness and convergence are derived in correspondence to a fixed value of the h sub spl infin norm attenuation level spl gamma finally a stepwise spl gamma switching strategy is devised to guarantee boundedness as well as asymptotic performance

hyperbolic cantori have dimension zero it is proved that cantori for area preserving twist maps have dimension zero only finitely many orbits of gaps and gap widths go to zero exponentially in each orbit if they are hyperbolic

on a resource allocation model with infinite horizon in this paper we treat a resource allocation model defined on an infinite interval we show that the solution of the corresponding problem with finite horizon cannot be extended to a solution of the infinite horizon problem since the resource allocation problem in the unmodified setting does not have a solution on an unbounded interval to change this situation we bring an additional state constraint into the model which contains a weight function the new problem called now the adapted resource allocation problem has an optimal solution which will be identified by means of the duality concept of klotzler

periodic phases in second order materials in 1984bernard coleman in consultation with v j mizel constructed a theory of materials for which the free energy density is influenced by both first and second spatial derivatives of the mass density u the goal was to see if such a theory would imply the possibility of occurrence of layered structures with interesting properties related to the spacing of the layers e g periodicity or quasiperiodicity the one dimensional isothermal free energy density for such second order materials was taken to be given by h u u u with h subject to certain inequalities the simplest prototypes for h have the form

a reduction of topological infinite horizon optimization to periodic optimization in a class of compact 2 manifolds abstract we consider a general class of infinite horizon optimization problems where the phase space is a two dimensional manifold satisfying the jordan curve theorem and the set of feasible curves satisfies general conditions similar to but weaker than the solution set of a control system we verify the existence of an optimal periodic solution for this class of problems applying this result we obtain two new results we generalize a previous result for discounted infinite horizon control problems and provide a poincare bendixson type result for continuous generalized semi flows

tracking periodic signals with the overtaking criterion the overtaking criterion is suggested to evaluate the tracking of periodic signals on an infinite horizon existence uniqueness and a feedback form are established the asymptotic dynamics of the solution and its relation to the asymptotic performance of the finite time optimizers are examined

on the cold drawing of polymers abstract when the amount of stretch in a taut fiber varies rapidly with distance z along the fiber axis the tension t on a cross section normal to the axis is not determined by only the temporal history of the local stretch but is affected by the variation of stretch with z here a study is made of the implications of a constitutive relation giving the tension in a polymeric fiber as a function of the local stretch the spatial derivative v z of the velocity and the first two spatial derivatives of the stretch z and zz when this relation is placed in the equation for balance of momentum in the axial direction dynamical equations are obtained whose equilibrium solutions for as a function of z can be rendered explicit the solutions describe necks bulges drawing configurations and periodic striations the assumption that motions resulting from slow changes in applied tension or length are homotopies formed from these equilibrium solutions is compatible with many of the observed properties of tension induced necking and cold drawing in polymeric fibers properties of non equilibrium solutions of the dynamical equations are also discussed here lyapunov functions appropriate to several types of boundary conditions including elongation under a dead load are constructed it is shown that the presence of viscous stresses has a strong effect on the types of traveling waves that can occur in long fibers a detailed discussion is given of a class of traveling waves called steady draws that correspond to the continuous drawing processes frequently employed to improve the stiffness and tenacity of synthetic fibers

asymptotic stability for a class of delay differential inclusions abstract in this work we provide sufficient conditions for the asymptotic stability of an equilibrium for a class of differential inclusions of finite retarded type where the right hand side is a set valued mapping having a bounded closed convex graph in particular our result includes linear differential inclusions in which the right hand side is a closed convex process this result partially generalizes an earlier result of leizarowitz 1985 siam j control optim 23 514 522 in the non delay case

computational structural mechanics and optimal control the simulation of substructural chain theory to linear quadratic optimal control problems the theory of optimal control and the theory of a substructural chain in static structural analysis are mutually simulated issues from the minimum potential energy variational principle of the substructural chain the generalized variational principle with two kinds of variables is derived first by comparing that generalized variational principle with the variational principle in lq control theory the simulation relation is established based on that relation the potential energy and mixed energy formulation of the algebraic riccati equations are derived then iterative algorithms are proposed which give the upper and lower bounds to the solution matrix by using the solutions of the positive and negative co ordinate algebraic riccati equations the canonical transformation matrices for the eigenproblems of the substructural chain and lq control are constructed respectively which reduce the eigenproblem to half size the properties of the solutions are analysed which establishes the basis for expansion solutions

homogenization of fully overdamped frenkel kontorova models in this paper we consider the fully overdamped frenkel kontorova model this is an infinite system of coupled first order odes each ode represents the microscopic evolution of one particle interacting with its neighbors and submitted to a fixed periodic potential after a proper rescaling a macroscopic model describing the evolution of densities of particles is obtained we get this homogenization result for a general class of frenkel kontorova models the proof is based on the construction of suitable hull functions in the framework of viscosity solutions

optical hamiltonians and symplectic twist maps abstract this paper concentrates on optical hamiltonian systems of t t n i e those for which hpp is a positive definite matrix and their relationship with symplectic twist maps we present theorems of decomposition by symplectic twist maps and existence of periodic orbits for these systems the novelty of these results resides in the fact that no explicit asymptotic condition is imposed on the system

one dimensional infinite horizon variational problems arising in continuum mechanics in this paper we study a variational problem for real valued functions defined on an infinite semiaxis of the line to wit given x 2 we seek a minimal solution to the problem minimize the functional given by i left w left cdot right right int limits 0 infty f left w left s right ddot w left s right right ds w in ax left upsilon in w loc 2 1 left 0 infty right left upsilon left 0 right dot upsilon left 0 right x right right p

exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant ori abstract an approximate renormalisation scheme is derived for the breakup of invariant tori of arbitrary winding ratio in hamiltonian systems of one and a half degrees of freedom similar to that of escande and doveil it is a free semi group with two generators this scheme is solved exactly for its orbits stable manifolds unstable manifolds and critical set various results are found including a cantor set of universal fractal diagrams the robustness of noble tori and a scaling law for areas near critical circles

rotation entropy and equilibrium states for a dynamical system x t and function f x rd we consider the corresponding generalised rotation set this is the convex subset of rd consisting of all integrals of f with respect to t invariant probability measures we study the entropy h e of rotation vectors e and relate this to the directional entropy lhl l of geller misiurewicz for x t a mixing subshift of finite type and f of summable variation we prove that if the rotation set is strictly convex then the functions h and h are in fact one and the same for those rotation sets which are not strictly convex we prove that 1h e and h e can differ only at non exposed boundary points e

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

aubry mather sets and birkhoff s theorem for geodesic flows on the two dimensional torus in this paper we state the graph property for incompressible continuouse tori invariant under goedesic flows of riemannian metrics on the two dimensional torus also our method gives a new proof of birkhoff s theorem for twist maps of the cylinder we prove that if there exist an invariant incompressible torus of geodesic flow with irrational rotation number then it necessarily contains the aubry mather set with this rotation number

strange non chaotic attractor in a quasiperiodically forced circle map abstract we show that in the quasiperiodically forced circle map strange non chaotic attractors can appear for non linearities far from the border of chaos the destruction of a two frequency quasiperiodic torus connected with the appearance of a strange non chaotic attractor is described in detail this strange non chaotic attractor is characterized by logarithmically slow diffusion of the phase it is shown that in this regime the high order phase locking states disappear and the rotation number varies rather smoothly with the parameters

global branches of multi bump periodic solutions of the swift hohenberg equation in this paper we study the existence of single and multi bump periodic solutions of a class of fourth order ordinary differential equations arising in problems of pattern formation measuring the tendency to form patterns by a parameter q we view the problem as a nonlinear eigenvalue problem with the use of analytical as well as numerical methods branches of periodic solutions are investigated both locally and globally

structure of approximate solutions for discrete time control systems arising in economic dynamics in this work we study the structure of approximate solutions of an autonomous discrete time control system with a compact metric space of states x which is a subset of a finite dimensional euclidean space this control system is described by a nonempty closed set x x which determines a class of admissible trajectories programs and by a bounded upper semicontinuous function v r1 which determines an optimality criterion we are interested in turnpike properties of the approximate solutions which are independent of the length of the interval for all sufficiently large intervals usually in economic dynamics the turnpike properties have been studied for systems such that all their good programs converge to a turnpike which was an interior point of in this paper we establish turnpike results for a large class of control systems for which the turnpike is not necessarily an interior point of

construction of analytic kam surfaces and effective stability bounds a class of analytic possibly time dependent hamiltonian systems withd degrees of freedom and the corresponding class of area preserving twist diffeomorphisms of the plane are considered implementing a recent scheme due to moser salamon and zehnder we provide a method that allows us to construct explicitly kam surfaces and hence to give lower bounds on their breakdown thresholds we then apply this method to the hamiltonianh y2 2 e cosx cos x t and to the map y x y e sinx x y e sinx obtaining with the aid of computer assisted estimations explicit approximations within an error of 10 5 of the golden mean kam surfaces for complex values of e with e less or equal than respectively 0 015 and 0 65 the experimental numerical values at which such surfaces are expected to disappear are about respectively 0 027 and 0 97 a possible connection between break down thresholds and singularities in the complex e plane is pointed out

destruction of invariant tori in pendulum type equations abstract in this paper we prove that if there exists an invariant torus with the rotation number 1 in the pendulum type equation x q 0 x t x for a given potential q 0 q 0 t x c t 2 and is a liouville number then for any neighborhood n q 0 of q 0 in the c topology there exists a potential q q t x n q 0 such that the system x q x t x does not admit any invariant torus with the rotation number 1 this confirms j moser s suggestion in bol soc brasil mat 20 1981 29 45

finite horizon h filter and its 2n algorithm a 2n algorithm will double a time or space step in each evaluation for initial value problem the 2n algorithm for the integration of filtering differential equation of the finite horizon h filter is presented in this paper since it is a boundary value problem within a time range a new 2n algorithm is introduced by merging two intervals each time so that the time interval is doubled in each evaluation if one divides the original time range into one million intervals 20 evaluations will complete the whole process owing to the extremely small initial time interval the first few terms of the taylor expansion of the interval matrices are sufficient for very accurate results since the filter gain matrices are the solution of the riccati differential equation and the existence of the solution depends on the induced norm the computation of critical value is reviewed first then according to the result and the prespecified performance index the suitable parameter 2 can be selected and the precise numerical solution of the riccati differential equation and the filtering differential equation can be obtained by using the 2n algorithm although the filtering equation is time varying the 2n algorithm for interval merging is given explicitly copyright 2001 john wiley sons ltd

on the influence of the kinetic energy on the stability of equilibria of natural lagrangian systems natural lagrangian systems t on r2 described by the equation frac d dt frac partial t partial dot q frac partial t partial q frac partial pi partial q are considered where t q q is a positive definite quadratic form in q and q has a critical point at 0 it is constructively proved that there exist a c potential energy and two c kinetic energies t and t such that the equilibrium q t 0 is stable for the system t and unstable for the system t equivalently it is established that for c natural systems the kinetic energy can influence the stability in the analytic category this is not true

percival variational principle for invariant measures and commensurate incommensurate phase transitions in one dimensional chains we prove for a one dimensional system of classical particles with potential energy u alpha gamma sum limits n left alpha v x n f x n 1 x n gamma right the existence of such a smooth function 0 0 that the system with potential energyu has the equilibrium state at the temperaturet 0 this is the incommensurate phase with the ratio of periods equal to the prescribed irrational number badly approximated by rational ones a simple geometric condition for the invariant curve of the corresponding dynamical system is established under which it is the support of the invariant measure minimizing percival s energy functional

amount of rotation about a point and the morse index for the case of exact area preserving monotone twist diffeomorphisms we give formulas relating the amount of rotation about an orbit and certain morse indices

spatial chaos in weakly dispersive and viscous media a nonperturbative theory of the driven kdv burgers equation abstract the asymptotic travelling wave solution of the kdv burgers equation driven by the long scale periodic driver is constructed the solution represents a shock train in which the quasi periodic sequence of dispersive shocks or soliton chains is interspersed by smoothly varying regions it is shown that the periodic solution which has the spatial driver period undergoes period doublings as the governing parameter changes two types of chaotic behavior are considered the first type is a weak chaos where only a small chaotic deviation from the periodic solution occurs the second type corresponds to the developed chaos where the solution ignores the driver period and represents a random sequence of uncorrelated shocks in the case of weak chaos the shock coordinate being repeatedly mapped over the driver period moves on a chaotic attractor while in the case of developed chaos it moves on a repeller both solutions depend on a parameter indicating the reference shock position in the shock train the structure of a one dimensional set to which this parameter belongs is investigated this set contains measure one intervals around the fixed points in the case of periodic or weakly chaotic solutions and it becomes a fractal in the case of strong chaos the capacity dimension of this set is calculated

stability of a turnpike phenomenon for approximate solutions of nonautonomous discrete time optimal control systems abstract we study turnpike properties of approximate solutions of nonautonomous discrete time optimal control systems which are determined by sequences of lower semicontinuous objective functions to have these properties means that the approximate solutions of the problems are determined mainly by the objective functions and are essentially independent of the choice of intervals and endpoint conditions except in regions close to the endpoints we show that these turnpike properties are stable under small perturbations of the objective functions

oscillating minimizers of a fourth order problem invariant under scaling by variational methods we prove the inequality int r u 2 dx int r u u 2 dx geq i int r u 4 dx quad forall u in l 4 r mbox such that u in l 2 r for some constant i in 9 64 1 4 this inequality is connected to lieb thirring type problems and has interesting scaling properties the best constant is achieved by sign changing minimizers of a problem on periodic functions but does not depend on the period moreover we completely characterize the minimizers of the periodic problem

angular dynamical spectra a new method for determining frequencies weak chaos and cantori we define the invariant spectra of rotation angles and twist angles angular dynamical spectra and study the properties of their moments angular moments in a model two dimensional map the angular moments give the main frequencies of the orbits a main frequency is defined both for a regular and chaotic orbit for kam curves around a centre this frequency corresponds to the rotation number inside islands of stability we obtain both the main frequency rotation number and the epicyclic frequency a fast detection of thin chaotic layers is obtained on the basis of the behaviour of the frequency curve we explore the resonant structure near a last kam boundary the secondary islands of various multiplicities forming farey sequences and the noble tori between them are located we find a criterion to determine whether various resonant chaotic zones communicate or are separated by invariant tori

aubry mather theory and hamilton jacobi equations we review and extend some results of jauslin kreiss moser and weinan e on the smooth approximation of mather sets

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

positivity and the attractor dimension in a fourth order reaction diffusion equation in this paper we investigate the semilinear partial differential equation ut fuxxxx uxx u 1 u2 with a view particularly to obtaining some insight into how one might establish positivity preservation results for equations containing fourth order spatial derivatives the maximum principle cannot be applied to such equations however progress can be made by employing some very recent best possible interpolation inequalities due to the third named author in which the interpolation constants are both explicitly known and sharp these are used to estimate the lx distance between u and 1 during the evolution a positivity preservation result can be obtained under certain restrictions on the initial datum we also establish an explicit two sided estimate for the fractal dimension of the attractor which is sharp in terms of the physical parameters

a turnpike result for discrete time optimal control systems in this chapter we study a turnpike property of approximate solutions for a general class of discrete time control systems without discounting and with a compact metric space of states this class of control systems is identified with a complete metric space of objective functions we show that for a generic objective function approximate solutions of the corresponding control system possess the turnpike property

interface interactions in modulated phases and upsilon points certain features in frenkel kontorova and other models of phases with a one dimensional modulation can be analyzed by assuming parallel interfaces separating sets of lattice planes belonging to two different phases and treating the free energy to create interfaces as well as the interaction of two three or more interfaces as phenomenological parameters a strategy employed by fisher and szpilka for interacting defects can be extended to the case of interfaces allowing a systematic study of the phase diagram by ignoring all interface interactions and then successively taking into account pair triple and higher order terms the possible phase diagrams which can occur near the point where 0 include various sorts of endpoints analogous to critical endpoints an accumulation point of first order transitions and triple points and a self similar structure which we call an upsilon point which turns out to be an accumulation point of an infinite number of segments of first order transition lines each of which terminates in two upsilon points

homotopy classes for stable connections between hamiltonian saddle focus equilibria for a class of hamiltonian systems in 4 the set of homoclinic and heteroclinic orbits which connect saddle focus equilibria is studied using a variational approach the oscillatory properties of a saddle focus equilibrium and the variational nature of the problem give rise to connections in many homotopy classes of the configuration plane punctured at the saddle foci this variational approach does not require any assumptions on the intersections of stable and unstable manifolds such as transversality moreover these connections are shown to be local minimizers of an associated action functional this result has applications to spatial pattern formation in a class of fourth order bistable evolution equations

lyapunov exponents of minimizing measures for globally positive diffeomorphisms in all dimensions the globally positive diffeomorphisms of the 2n dimensional annulus are important because they represent what happens close to a completely elliptic periodic point of a symplectic diffeomorphism where the torsion is positive definite for these globally positive diffeomorphisms an aubry mather theory was developed by garibaldi and thieullen that provides the existence of some minimizing measures using the two green bundles g and g that can be defined along the support of these minimizing measures we will prove that there is a deep link between the angle between g and g along the support of the considered measure mu the size of the smallest positive lyapunov exponent of mu the tangent cone to the support of mu

recent developments in the theory of hamiltonian systems area preserving mappings of an annulus occur as poincare mappings of hamiltonian systems they were studied extensively by g d birkhoff recently aubry and mather investigated the subclass of so called monotone twist mappings for which they constructed independently closed invariant cantor sets their work led to important new results their theory is discussed and related to hamiltonian systems satisfying a legendre condition the connection of this theory with the stability problem kam theory and in particular the disintegration of invariant tori is discussed various constructions of mather sets are explained in which minimal solutions of variational problems play a central role this theory has a close relation to the differential geometric investigations by morse and hedlund on geodesics on two dimensional surfaces