error estimates on the approximate finite volume solution of convection diffusion equations with general boundary conditions we study here the convergence of a finite volume scheme for a diffusion convection equation on an open bounded set of r dim dim 2 or 3 for which we consider dirichlet neumann or robin boundary conditions we consider unstructured meshes which include voronoi or triangular meshes we use for the diffusion term an s points where s is the number of sides of each cell finite volume scheme and for the convection term an upstream finite volume scheme assuming the exact solution at least in h2 we prove error estimates in a discrete h 1 0 norm of order the size of the mesh discrete poincare inequalities then allow one to prove error estimates in the l2 norm

area preserving surface diffeomorphisms we prove some generic properties for cr r 1 2 area preserving diffeomorphism on compact surfaces the main result is that the union of the stable or unstable manifolds of hyperbolic periodic points are dense in the surface this extends the result of franks and le calvez 10 on s2 to general surfaces the proof uses the theory of prime ends and lefschetz fixed point theorem

a symplectic fixed point theorem for cpn two symplectic diffeomorphisms 0 1 of a symplectic manifold x are said to be homologous if there exists a smooth homotopy 1 t 0 1 of symplectic diffeomorphisms between them such that the timedependent vector field t defined byd dt t t o t is a globally hamiltonian vector field for allt i e there exists a smooth real valued timedependent hamiltonian functionh x t onx x 0 1 such that t dh t whereht h x t

h convergence and numerical schemes for elliptic equations we study the convergence of two coupled numerical schemes which are a discretization of a so called elliptic hyperbolic system only weak convergence properties are proved on the discrete diffusion of the elliptic problem and an adaptation of the h convergence method gives a convergence property of the elliptic part of the scheme the limit of the approximate solution is then the solution of an elliptic problem the diffusion of which is not in the general case the h limit of the discrete diffusion in a particular case a kind of weak limit is then obtained for the hyperbolic equation

subharmonic solutions of hamiltonian equations on tori let the torus t2n be equipped with the standard symplectic structure and a periodic hamiltonian dt e c3 sx x t2n r we look for periodic orbits of the hamiltonian flow u t j vdt t a subharmonic solution is a periodic orbit with minimal period an integral multiple m of the period of dt with m 1 we prove that if the hamiltonian flow has only finitely many orbits with the same period as dt then there are subharmonic solutions with arbitrarily high minimal period thus there are always infinitely many distinct periodic orbits the results proved here were proved in the nondegenerate case by conley and zehnder and in the case n 1 by le calvez

distributed control for identical dynamically coupled systems a decomposition approach we consider the problem of designing distributed controllers for a class of systems which can be obtained from the interconnection of a number of identical subsystems if the state space matrices of these systems satisfy a certain structural property then it is possible to derive a procedure for designing a distributed controller which has the same interconnection pattern as the plant this procedure is basically a multiobjective optimization under linear matrix inequality constraints with system norms as performance indices the explicit expressions for computing these controllers are given for both h infin or h 2 performance and both for static state feedback and dynamic output feedback in discrete time at the end of the paper two application examples illustrate the effectiveness of the approach

sinc galerkin method for solving biharmonic problems there are many techniques available to numerically solve the biharmonic equation in this paper we show that the sinc galerkin method is a very effective tool in numerically solving this equation hermite interpolation is used to treat the nonhomogeneous boundary conditions our method is tested on examples and comparisons with other methods are made it is shown that the sinc galerkin method yields good results even when singularities occur at the boundaries

new proofs of some results of nielsen given a compact oriented surface m with negative euler characteristic and a homeomorphism z m2 m2 what is the best representative cp m2 m2 in the isotopy class of s thurston s answered this question by defining pseudo anosov homeomorphisms a generalization of anosov diffeomorphisms on t2 which may be characterized as follows the homeomorphism rp is pseudo anosov iff there is a pair of transverse measured geodesic laminations i and au which intersect each closed nonperipheral geodesic in h4 which are topologically preserved by cp and which have their respective transverse measures multiplied under the action of cp by l n and d for some l 1 thurston showed that cp m m2 can be pieced together from homeomorphisms of subsurfaces which are either periodic or pseudoanosov more precisely thurston proved theorem 0 1 the preprint s provides an introduction to this theorem describing many of the useful properties of pseudo anosov diffeomorphisms the proof outlined in s is contained in 111

from euler ritz and galerkin to modern computing the so called ritz galerkin method is one of the most fundamental tools of modern computing its origins lie in hilbert s direct approach to the variational calculus of euler lagrange and in the thesis of walther ritz who died 100 years ago at the age of 31 after a long battle with tuberculosis the thesis was submitted in 1902 in gottingen during a period of dramatic developments in physics ritz tried to explain the phenomenon of balmer series in spectroscopy using eigenvalue problems of partial differential equations on rectangular domains while this physical model quickly turned out to be completely obsolete his mathematics later enabled him to solve difficult problems in applied sciences he thereby revolutionized the variational calculus and became one of the fathers of modern computational mathematics we will see in this article that the path leading to modern computational methods and theory involved a long struggle over three centuries requiring the efforts of many great mathematicians

hamiltonian pseudo rotations of projective spaces the main theme of the paper is the dynamics of hamiltonian diffeomorphisms of mathbb c mathbb p n with the minimal possible number of periodic points equal to n 1 by arnold s conjecture called here hamiltonian pseudo rotations we prove several results on the dynamics of pseudo rotations going beyond periodic orbits using floer theoretical methods one of these results is the existence of invariant sets in arbitrarily small punctured neighborhoods of the fixed points partially extending a theorem of le calvez and yoccoz and of franks and misiurewicz to higher dimensions the other is a strong variant of the lagrangian poincare recurrence conjecture for pseudo rotations we also prove the c 0 rigidity of pseudo rotations with exponentially liouville mean index vector this is a higher dimensional counterpart of a theorem of bramham establishing such rigidity for pseudo rotations of the disk

finite volume schemes for the biharmonic problem on general meshes finite volume schemes for the approximation of a biharmonic problem with dirichlet boundary conditions are constructed and analyzed first on grids which satisfy an orthogonality condition and then on general possibly non conforming meshes in both cases the piece wise constant approximate solution is shown to converge in l2 to the exact solution similar results are shown for the discrete approximate of the gradient and the discrete approximate of the laplacian of the exact solution error estimates are also derived these results are confirmed by numerical results

robust stability of a multi agent system under arbitrary and time varying communication topologies and communication delays this technical note considers formation control of a group of identical agents that can communicate with each other a necessary and sufficient condition for robust stability in the case of arbitrary time invariant communication topologies and sufficient conditions in the case of arbitrary time varying topology and communication delays are derived that reduce the stability analysis and controller design problems to analysis or synthesis respectively for a single agent

rotation vectors and fixed points of area preserving surface diffeomorphisms we consider the homological rotation vectors for area preserving diffeomorphisms of compact surfaces which are homotopic to the identity there are two main results the first is that if 0 is in the interior of the convex hull of the rotation vectors for such a diffeomorphism then f has a fixed point of positive index the second result asserts that if f has a vanishing mean rotation vector then f has a fixed point of positive index there are several applications including a new proof of the arnold conjecture for area preserving diffeomorphisms of compact surfaces in this paper we investigate area preserving diffeomorphisms of compact surfaces we are concerned with rotation vectors defined in terms of homology which can be associated to the points of the surface there are two main results the first is that if f is an area preserving diffeomorphism of a compact surface which is homotopic to the identity and 0 is in the interior of the convex hull of the rotation vectors of f then f has a fixed point of positive index the second result concerns the mean rotation vector of f it asserts that if this vector vanishes then f has a fixed point of positive index a special case of this second result when the surface in question is a surface of genus zero was proved in f5 in 6 we give several applications including a new proof of the arnold conjecture for area preserving diffeomorphisms of compact surfaces

variational methods in relativistic quantum mechanics this review is devoted to the study of stationary solutions of lin ear and nonlinear equations from relativistic quantum mechanics involving the dirac operator the solutions are found as critical points of an energy func tional contrary to the laplacian appearing in the equations of nonrelativistic quantum mechanics the dirac operator has a negative continuous spectrum which is not bounded from below this has two main consequences first the energy functional is strongly indefinite second the euler lagrange equations are linear or nonlinear eigenvalue problems with eigenvalues lying in a spectral gap between the negative and positive continuous spectra moreover since we work in the space domain r 3 the palais smale condition is not satisfied for these reasons the problems discussed in this review pose a challenge in the calculus of variations the existence proofs involve sophisticated tools from nonlinear analysis and have required new variational methods which are now applied to other problems in the first part we consider the fixed eigenvalue problem for models of a free self interacting relativistic particle they allow to describe the localized state of a spin 1 2 particle a fermion which propagates without changing its shape this includes the soler models and the maxwell dirac or klein gordon dirac equations the second part is devoted to the presentation of min max principles al lowing to characterize and compute the eigenvalues of linear dirac operators with an external potential in the gap of their essential spectrum many con sequences of these min max characterizations are presented among them a new kind of hardy like inequalities and a stable algorithm to compute the eigenvalues in the third part we look for normalized solutions of nonlinear eigenvalue problems the eigenvalues are lagrange multipliers lying in a spectral gap we review the results that have been obtained on the dirac fock model which is a nonlinear theory describing the behavior of n interacting electrons in an external electrostatic field in particular we focus on the problematic definition of the ground state and its nonrelativistic limit in the last part we present a more involved relativistic model from quan tum electrodynamics in which the behavior of the vacuum is taken into ac count it being coupled to the real particles the main interesting feature of this model is that the energy functional is now bounded from below providing us with a good definition of a ground state

a fast direct solver for the biharmonic problem in a rectangular grid we present a fast direct solver methodology for the dirichlet biharmonic problem in a rectangle the solver is applicable in the case of the second order stephenson scheme j w stephenson j comput phys 55 1984 pp 65 80 as well as in the case of a new fourth order scheme which is discussed in this paper and is based on the capacitance matrix method b l buzbee and f w dorr siam j numer anal 11 1974 pp 1136 1150 p bjorstad siam j numer anal 20 1983 pp 59 71 the discrete biharmonic operator is decomposed into two components the first is a diagonal operator in the eigenfunction basis of the laplacian to which the fft algorithm is applied the second is a low rank perturbation operator given by the capacitance matrix which is due to the deviation of the discrete operators from diagonal form the sherman morrison formula g h golub and c f van loan matrix computations 3rd ed john hopkins university press baltimore md 1996 is applied to obtain a fast solution of the resulting linear system of equations

rotation numbers and instability sets translation and rotation numbers have played an interesting and important role in the qualitative description of various dynamical systems in this exposition we are especially interested in applications which lead to proofs of periodic motions in various kinds of dynamics on the annulus the applications include billiards and geodesic flows going beyond this simple qualitative invariant in the study of the dynamics of area preserving annulus maps g d birkhoff was led to the concept of regions of instability for twist maps we discuss the closely related notion of instability sets for a generic area preserving surface diffeomorphism and develop their properties

analysis and convergence of the mac scheme i the linear problem the mac marker and cell discretization of fluid flow is analysed for the stationary stokes equations it is proved that the discrete approximations do in fact converge to the exact solutions of the flow equations estimates using mesh dependent norms analogous to the standard bf h 1 and l 2 norms are given for the velocity and pressure respectively

the unregularized gradient flow of the symplectic action the symplectic action can be defined on the space of smooth paths in a symplectic manifold p which join two lagrangian submanifolds of p to pursue a new approach to the variational theory of this function we define on a subset of the path space the flow whose trajectories are given by the solutions of the cauchy riemann equation with respect to a suitable almost complex structure on p in particular we prove compactness and transversality results for the set of bounded trajectories

periodic orbits of hamiltonian homeomorphisms of surfaces john franks and michael handel fh2 have recently proved that any nontrivial hamiltonian diffeomorphism of a closed surface of genus at least one has periodic orbits of arbitrarily large period they proved a similar result for a nontrivial area preserving diffeomorphism of a sphere with at least three fixed points we extend these results to the case of the homeomorphisms when the genus is at least one we prove moreover that the periodic orbits may be chosen contractible if the set of contractible fixed points is contained in a disk when the surface is a sphere we extend the result to the case of a nontrivial homeomorphism with no wandering points the proofs make use of an equivariant foliated version of brouwer s plane translation theorem see b proposition 2 1 and some properties of the linking number of fixed points

a priori degeneracy of one dimensional rotation sets for periodic point free torus maps diffeomorphisms of the two torus that are isotopic to the identity have rotation sets that are convex compact subsets of the plane we show that certain line segments including all rationally sloped segments with no rational points cannot be realized as a rotation set

a compact difference scheme for the biharmonic equation in planar irregular domains we present a finite difference scheme applicable to general irregular planar domains to approximate the biharmonic equation the irregular domain is embedded in a cartesian grid in order to approximate delta 2 phi at a grid point we interpolate the data on the irregular stencil by a polynomial of degree six the finite difference scheme is delta 2 q phi 0 0 where q phi is the interpolation polynomial the interpolation polynomial is not uniquely determined we present a method to construct such an interpolation polynomial and prove that our construction is second order accurate for a regular stencil m ben artzi j p croisille and d fishelov siam j sci comput 31 2008 pp 303 333 shows that the proposed interpolation polynomial is fourth order accurate we present some suitable numerical examples

brief paper synchronization in networks of identical linear systems the paper investigates the synchronization of a network of identical linear state space models under a possibly time varying and directed interconnection structure the main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected the result can be interpreted as a generalization of classical consensus algorithms stronger conditions are shown to be sufficient but to some extent also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature

h convergence and numerical schemes for elliptic problems we study the convergence of two coupled numerical schemes which are a discretization of a so called elliptic hyperbolic system only weak convergence properties are proved on the discrete diffusion of the elliptic problem and an adaptation of the h convergence method gives a convergence property of the elliptic part of the scheme the limit of the approximate solution is then the solution of an elliptic problem the diffusion of which is not in the general case the h limit of the discrete diffusion in a particular case a kind of weak limit is then obtained for the hyperbolic equation

morse theory for fixed points of symplectic diffeomorphisms on demontre le cas particulier suivant de la conjecture de arnold sur les points fixes d une deformation exacte d une variete symplectique compacte close p si 2 p 0 et tous les points fixes de sont non degeneres alors leur nombre est plus grand ou egal a la somme des nombres de betti de p par rapport aux coefficients z 2

hp version interior penalty dgfems for the biharmonic equation we construct hp version interior penalty discontinuous galerkin finite element methods dgfems for the biharmonic equation including symmetric and nonsymmetric interior penalty discontinuous galerkin methods and their combinations semisymmetric methods our main concern is to establish the stability and to develop the a priori error analysis of these methods we establish error bounds that are optimal in h and slightly suboptimal in p the theoretical results are confirmed by numerical experiments

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

growth of maps distortion in groups and symplectic geometry in the present paper we study two sequences of real numbers associated to a symplectic diffeomorphism the uniform norm of the differential of its n th iteration the word length of its n th iteration where we assume that our diffeomorphism lies in a finitely generated group of symplectic diffeomorphisms we find lower bounds for the growth rates of these sequences in a number of situations these bounds depend on the symplectic geometry of the manifold rather than on the specific choice of a diffeomorphism they are obtained by using recent results of schwarz on floer homology as an application we prove non existence of certain non linear symplectic representations for finitely generated groups

on the lusternik schnirelmann category of symplectic manifolds and the arnold conjecture in arn appendix 9 arnold proposed a beautiful conjecture concerning the relation between the number of fixed points of certain i e exact or hamiltonian selfdiffeomorphisms of a closed symplectic manifold m and the minimum number of critical points of any smooth c function on m the first author succeeded in proving this form of the arnold conjecture r2 under the hypothesis that and c1 vanish on all spherical homology classes and that there is equality between the lusternik schnirelmann category of m and the dimension of m in this paper we use a fundamental property of category weight to show that for any closed symplectic manifold whose symplectic form vanishes on the image of the hurewicz map the required equality holds thus we show that the original form of the arnold conjecture holds for all symplectic manifolds having 2 m 0 c1 2 m

a mixed finite volume element method based on rectangular mesh for biharmonic equations this paper presents a mixed finite volume element scheme based on rectangular partition for solving biharmonic equations it also gives a kind of adaptive uzawa iteration method for the scheme it is rigorously proved that the scheme has first order accuracy in h1 semi norm and l2 norm according to the characteristics of the scheme finally two numerical examples illustrate the effectiveness of the method

some results of hamiltonian homeomorphisms on closed aspherical surfaces abstract on closed symplectically aspherical manifolds by using floer homology schwarz proved a classical result i e that the action function of a nontrivial hamiltonian diffeomorphism is not constant in this article we generalize schwarz s theorem to the c 0 case on closed aspherical surfaces our methods are purely topological and involve the theory of transverse foliations for dynamical systems of surfaces and the recent progress inspired by le calvez as an application we prove that the contractible fixed points set and consequently the fixed points set of a nontrivial hamiltonian homeomorphism is not connected we also get a similar result for an orientation preserving nonwandering point homeomorphism of the two sphere in the end we give further applications based on the c 0 schwarz theorem

a c 0 counterexample to the arnold conjecture the arnold conjecture states that a hamiltonian diffeomorphism of a closed and connected symplectic manifold m omega must have at least as many fixed points as the minimal number of critical points of a smooth function on m it is well known that the arnold conjecture holds for hamiltonian homeomorphisms of closed symplectic surfaces the goal of this paper is to provide a counterexample to the arnold conjecture for hamiltonian homeomorphisms in dimensions four and higher more precisely we prove that every closed and connected symplectic manifold of dimension at least four admits a hamiltonian homeomorphism with a single fixed point

commuting hamiltonians and hamilton jacobi multi time equations the aim of this paper is twofold first of all we show that the c 0 limit of a pair of commuting hamiltonians commute this means on one hand that if the limit of the hamiltonians is smooth the poisson bracket of their limit still vanishes and on the other hand that we may define commutation for c 0 functions the second part of the paper deals with solving multi time hamilton jacobi equations using variational solutions this extends the work of barles and tourin in the viscosity case to include the case of c 0 hamiltonians and removes their convexity assumption provided we are in the framework of variational solutions

strictly toral dynamics this article deals with nonwandering e g area preserving homeomorphisms of the torus mathbb t 2 which are homotopic to the identity and strictly toral in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane this includes all homeomorphisms which have a rotation set with nonempty interior we define two types of points inessential and essential the set of inessential points operatorname ine f is shown to be a disjoint union of periodic topological disks elliptic islands while the set of essential points operatorname ess f is an essential continuum with typically rich dynamics the chaotic region this generalizes and improves a similar description by jager the key result is boundedness of these elliptic islands which allows among other things to obtain sharp uniform bounds of the diffusion rates we also show that the dynamics in operatorname ess f is as rich as in mathbb t 2 from the rotational viewpoint and we obtain results relating the existence of large invariant topological disks to the abundance of fixed points

geodesics on s2 and periodic points of annulus homeomorphisms we show that an area preserving homeomorphism of the open or closed annulus which has at least one periodic point must in fact have infinitely many interior periodic points a consequence is the theorem that every smooth riemannian metric ons2 with positive gaussian curvature has infinitely many distinct closed geodesics

euler maclaurin with remainder for a simple integral polytope we give an euler maclaurin formula with remainder for the sum of the values of a smooth function on the integral points in a simple integral polytope we prove this formula by elementary methods

generalizations of the poincare birkhoff theorem in this article we prove some generalizations of the classical poincar birkhoff theorem on area preserving homeomorphisms of the annulus which satisfy a boundary twist condition the work of g d birkhoff on this theorem and its applications can be found in b1 b2 and chapter v of b3 a more modern treatment can be found in b n we prove a theorem for the open annulus a s1 x 0 1 since as we will see the theorem for the closed annulus can easily be obtained from this result for the open annulus however it is not immediately obvious what should be the analogue of the twist condition it turns out that the most general hypothesis and the most natural from the point of view of our proof involves the notion of positively and negatively returning disks for some lift of f to the covering space a r x 0 1 more precisely if f a a is a lift of f a a we will say that the e is a positively returning disk for f if there is an open disk u c a such that f u n u 0 and fp u n u k 0 forsome n k 0 here u k denotes the set x k t i x t e u thus u is disjoint from its image but under iteration by f returns to a positive translate of itself a negatively returning disk is defined similarly but with k 0 such that fl u n u 0 in section 2 we prove the following

the conley conjecture for hamiltonian systems on the cotangent bundle and its analogue for lagrangian systems abstract in this paper the conley conjecture which was recently proved by franks and handel j franks m handel periodic points of hamiltonian surface diffeomorphism geom topol 7 2003 713 756 for surfaces of positive genus hingston n hingston subharmonic solutions of hamiltonian equations on tori ann math in press for tori and ginzburg v l ginzburg the conley conjecture arxiv math sg 0610956v1 for closed symplectically aspherical manifolds is proved for c 1 hamiltonian systems on the cotangent bundle of a c 3 smooth compact manifold m without boundary of a time 1 periodic c 2 smooth hamiltonian h r t m r which is strongly convex and has quadratic growth on the fibers namely we show that such a hamiltonian system has an infinite sequence of contractible integral periodic solutions such that any one of them cannot be obtained from others by iterations if h also satisfies h t q p h t q p for any t q p r t m it is shown that the time 1 map of the hamiltonian system if exists has infinitely many periodic points siting in the zero section of t m if m is c 5 smooth and dim m 1 h is of c 4 class and independent of time t then for any 0 the corresponding system has an infinite sequence of contractible periodic solutions of periods of integral multiple of such that any one of them cannot be obtained from others by iterations or rotations these results are obtained by proving similar results for the lagrangian system of the fenchel transform of h l r t m r which is proved to be strongly convex and to have quadratic growth in the velocities yet

consensus of multiple nonholonomic chained form systems abstract consensus problems of multiple nonholonomic systems are considered in this paper this problem is simplified into consensus problems of two subsystems based on the cascaded structure of nonholonomic chained form systems continuous and hybrid distributed controllers have been constructed for these two subsystems respectively based on the theory of cascaded systems consensus of multiple nonholonomic chained form systems can be realized using the methodology proposed in this paper no matter whether the group reference signal is persistently exciting or not different to previous assumptions on group reference such as persistent excitation or converging to nonzero constant the condition on the group reference signal have been further relaxed in this paper simulation results using matlab have illustrated the effectiveness of the results presented in this paper

controller design for plants with structured uncertainty this paper addresses the problem of designing feedback controllers to achieve good performance in the presence of structured plant uncertainty and bounded but unknown disturbances a general formulation for the performance robustness problem is presented and exact computable conditions are furnished these conditions are then utilized for synthesizing robust controllers which involves solving l1 optimization problems these solutions are computed using the duality theory of lagrange multipliers approximations and computational issues are discussed

some quantitative results in mathcal c 0 c 0 symplectic geometry this paper proceeds with the study of the mathcal c 0 symplectic geometry of smooth submanifolds as initiated in humiliere et al duke math j 164 4 767 799 2015 and opshtein ann sci ec norm super 42 5 857 864 2009 with the main focus on the behaviour of symplectic homeomorphisms with respect to numerical invariants like capacities our main result is that a symplectic homeomorphism may preserve and squeeze codimension 4 symplectic submanifolds mathcal c 0 flexibility while this is impossible for codimension 2 symplectic submanifolds mathcal c 0 rigidity we also discuss mathcal c 0 invariants of coistropic and lagrangian submanifolds proving some rigidity results and formulating some conjectures we finally formulate an eliashberg gromov mathcal c 0 rigidity type question for submanifolds which we solve in many cases our main technical tool is a quantitative h principle result in symplectic geometry

the conley conjecture we prove the conley conjecture for a closed symplectically aspherical symplectic manifold a hamiltonian diffeomorphism of such a manifold has infinitely many periodic points more precisely we show that a hamiltonian diffeomorphism with finitely many fixed points has simple periodic points of arbitrarily large period this theorem generalizes for instance a recent result of hingston establishing the conley conjecture for tori

solutions of the cohomological equation for area preserving flows on compact surfaces of higher genus let f be a local homeomorphism of the plane with a fixed point z which is a locally maximal invariant set and which is neither a sink nor a source we prove that there are two integers q 1 and r 1 such that the sequence i fk z of the indices at z of the iterates of f satisfy i fk z 1 rq if k is a multiple of q and i fk z 1 otherwise as a corollary we deduce that there is no minimal homeomorphism on the infinite annulus or more generally on the two dimensional sphere minus a finite set of points we also construct for a local homeomorphism f as above a topological invariant which is a cyclically ordered set with an automorphism on it this allows us in particular to define a rotation number for f rational of denominator q

symplectic fixed points and holomorphic spheres letp be a symplectic manifold whose symplectic form integrated over the spheres inp is proportional to its first chern class on the loop space ofp we consider the variational theory of the symplectic action function perturbed by a hamiltonian term in particular we associate to each isolated invariant set of its gradient flow an abelian group with a cyclic grading it is shown to have properties similar to the homology of the conley index in locally compact spaces as an application we show that if the fixed point set of an exact diffeomorphism onp is nondegenerate then it satisfies the morse inequalities onp we also discuss fixed point estimates for general exact diffeomorphisms

the monopole equations in topological yang mills we twist the monopole equations of seiberg and witten and show how these equations are realized in topological yang mills theory a floer derivative and a morse functional are found and are used to construct a unitary transformation between the usual floer cohomologies and those of the monopole equations furthermore these equations are seen to reside in the vanishing self dual curvature condition of an osp 1 2 bundle alternatively they may be seen arising directly from a vanishing self dual curvature condition on an su 2 bundle in which the fermions are realized as spanning the tangent space for a specific background

cuplength estimates on lagrangian intersections on demontre l estimation suivante sur des intersections lagrangiennes si l est une sous variete lagrangienne de p avec 2 p l 0 et l est obtenue a partir de l par un diffeomorphisme exact de p alors le nombre d elements de l l est superieure ou egale a la longueur de calotte de p

symplectically degenerate maxima via generating functions we provide a simple proof of a theorem due to nancy hingston asserting that symplectically degenerate maxima of any hamiltonian diffeomorphism phi of the standard symplectic 2d torus are non isolated contractible periodic points or their action is a non isolated point of the average action spectrum of phi our argument is based on generating functions

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper