morse theory for periodic solutions of hamiltonian systems and the maslov index in this paper we prove morse type inequalities for the contractible 1 periodic solutions of time dependent hamiltonian differential equations on those compact symplectic manifolds m for which the symplectic form and the first chern class of the tangent bundle vanish over q m the proof is based on a version of infinite dimensional morse theory which is due to floer the key point is an index theorem for the fredholm operator which plays a central role in floer homology the index formula involves the maslov index of nondegenerate contractible periodic solutions this maslov index plays the same role as the morse index of a nondegenerate critical point does in finite dimensional morse theory we shall use this connection between floer homology and maslov index to establish the existence of infinitely many periodic solutions having integer periods provided that every i periodic solution has at least one floquet multiplier which is not equal to 1

on the maslov index in this paper we give four definitions of maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other moreover relationships of several symplectic and differential geometric analytic and topological invariants including triple maslov indices eta invariants spectral flow and signatures of quadratic forms to the maslov index are developed and formulae relating them are given the broad presentation is designed with a view to applications both in geometry and in analysis 1994 john wiley sons inc

optimal surface segmentation in volumetric images a graph theoretic approach efficient segmentation of globally optimal surfaces representing object boundaries in volumetric data sets is important and challenging in many medical image analysis applications we have developed an optimal surface detection method capable of simultaneously detecting multiple interacting surfaces in which the optimality is controlled by the cost functions designed for individual surfaces and by several geometric constraints defining the surface smoothness and interrelations the method solves the surface segmentation problem by transforming it into computing a minimum s hbox t cut in a derived arc weighted directed graph the proposed algorithm has a low order polynomial time complexity and is computationally efficient it has been extensively validated on more than 300 computer synthetic volumetric images 72 ct scanned data sets of different sized plexiglas tubes and tens of medical images spanning various imaging modalities in all cases the approach yielded highly accurate results our approach can be readily extended to higher dimensional image segmentation

automatic model based segmentation of the heart in ct images automatic image processing methods are a pre requisite to efficiently analyze the large amount of image data produced by computed tomography ct scanners during cardiac exams this paper introduces a model based approach for the fully automatic segmentation of the whole heart four chambers myocardium and great vessels from 3 d ct images model adaptation is done by progressively increasing the degrees of freedom of the allowed deformations this improves convergence as well as segmentation accuracy the heart is first localized in the image using a 3 d implementation of the generalized hough transform pose misalignment is corrected by matching the model to the image making use of a global similarity transformation the complex initialization of the multicompartment mesh is then addressed by assigning an affine transformation to each anatomical region of the model finally a deformable adaptation is performed to accurately match the boundaries of the patient s anatomy a mean surface to surface error of 0 82 mm was measured in a leave one out quantitative validation carried out on 28 images moreover the piecewise affine transformation introduced for mesh initialization and adaptation shows better interphase and interpatient shape variability characterization than commonly used principal component analysis

multiple brake orbits for some classes of singular hamiltonian systems from which one can easily construct a periodic solution of period 2t by reflecting q around t 0 t if q x e e 1 v x hj is homeomorphic to a ball then the existence of one brake orbit is a classical result of seifert 11 generalizations of that result as well as alternative proofs were given in 2 6 141 in the case in which the topology of sz is richer then the existence of multiple solutions has been proved by bolotin and kozlov in 7 see also 8 in this paper we are mainly concerned with the case in which the potential v has singularities inside 2 in the sense that v x co as x x e ai and the topology of q is nontrivial more precisely in section 2 we shall assume that sz has a certain number of holes k and that v behaves like lxi o1 with 0 cx 2 near x 0 and we shall show that 1 3 has at least k classical brake orbits let us point out that the main interest of this result lies in the fact that we are able to prove that the solutions we find are classical ones that is they do not collide with the singularity while most of the papers dealing with existence of fixed energy 9 or fixed period lo solutions for singular potentials only prove existence of generalized solutions that is solutions which can collide with the singularity existence of a noncollision periodic solution for a singular potential

index and stability of symmetric periodic orbits in hamiltonian systems with application to figure eight orbit in this paper using the maslov index theory in symplectic geometry we build up some stability criteria for symmetric periodic orbits in a hamiltonian system which is motivated by the recent discoveries in the n body problem the key ingredient is a generalized bott type iteration formula for periodic solution in the presence of finite group action on the orbit for second order system we prove under general boundary conditions the close formula for the relationship between the morse index of an orbit in a lagrangian system and the maslov index of the fundamental solution for the corresponding orbit in its hamiltonian system counterpart and the boundary conditions cover the cases which appeared in the n body problem as an application we consider the stability problem of the celebrated figure eight orbit due to chenciner and montgomery in the planar three body problem with equal masses and we clarify the relationship between linear stability and its variational nature on various loop spaces the basic idea is as follows the variational characterization of the figure eight orbit provides information about its morse index based on its relation to the maslov index our stability criteria come into play

multiple periodic solutions of hamiltonian systems with prescribed energy abstract consider the periodic solutions of autonomous hamiltonian systems x j h x on the given compact energy hypersurface h 1 1 if is convex or star shaped there have been many remarkable contributions for existence and multiplicity of periodic solutions it is a hard problem to discuss the multiplicity on general hypersurfaces of contact type in this paper we prove a multiplicity result for periodic solutions on a special class of hypersurfaces of contact type more general than star shaped ones

relative morse index and multiple brake orbits of asymptotically linear hamiltonian systems in the presence of symmetries in this paper we define a relative morse index for two continuous symmetric matrices paths in r 2n satisfying condition b1 and study its relation with the maslov type indices under brake orbit boundary value of these two symmetric matrices paths as applications using this relation we obtain a multiple existence of periodic brake orbit solutions of asymptotically linear hamiltonian system in the presence of symmetries

shape registration in implicit spaces using information theory and free form deformations we present a novel variational and statistical approach for shape registration shapes of interest are implicitly embedded in a higher dimensional space of distance transforms in this implicit embedding space registration is formulated in a hierarchical manner the mutual information criterion supports various transformation models and is optimized to perform global registration then a b spline based incremental free form deformations iffd model is used to minimize a sum of squared differences ssd measure and further recover a dense local nonrigid registration field the key advantage of such framework is twofold 1 it naturally deals with shapes of arbitrary dimension 2d 3d or higher and arbitrary topology multiple parts closed open and 2 it preserves shape topology during local deformation and produces local registration fields that are smooth continuous and establish one to one correspondences its invariance to initial conditions is evaluated through empirical validation and various hard 2d 3d geometric shape registration examples are used to show its robustness to noise severe occlusion and missing parts we demonstrate the power of the proposed framework using two applications one for statistical modeling of anatomical structures another for 3d face scan registration and expression tracking we also compare the performance of our algorithm with that of several other well known shape registration algorithms

symplectic topology and hamiltonian dynamics on etudie des applications symplectiques non lineaires capacites symplectiques construction d une capacite symplectique problemes de plongement problemes de rigidite

closed characteristics on non compact hypersurfaces in r 2n viterbo demonstrated that any 2n 1 dimensional compact hypersur face m r 2n of contact type has at least one closed characteristic this result proved the weinstein conjecture for the standard symplectic space r 2n various extensions of this theorem have been obtained since all for compact hypersurfaces in this paper we consider non compact hypersurfaces m r 2n coming from mechanical hamiltonians and prove an analogue of viterbo s result the main result provides a strong connection between the top half homology groups hi m i n 2n 1 and the existence of closed characteristics in the non compact case including the compact case

closed characteristics on partially symmetric compact convex hypersurfaces in r2n abstract in this paper we study the multiplicity of closed characteristics on partially symmetric convex compact hypersurfaces in r 2n the main ingredient of the proof is a new p index function and its iteration theory for symplectic matrix paths and some symplectic orthogonal matrix p this theory yields estimates on this multiplicity via index estimates for a new type of iterations of any symplectic matrix path 0 sp 2n defined by t p t p for any t 0

symmetric closed characteristics on symmetric compact convex hypersurfaces in r 2n in this article let r2n be a compact convex hypersurface which is symmetric with respect to the origin where n 2 or 3 we prove that if carries exactly n geometrically distinct closed characteristics then all of them must be symmetric

on the existence of periodic solutions for a class of symetric hamiltonian systems abstract hamiltonian systems are used to model the motion of discrete mechanical systems this paper establishes the existence of periodic solutions for a class of such systems the method developed to prove existence should be useful for other such problems keywords minimax technique ordinary differential equations and variational problem

multiple brake orbits on convex hypersurfaces under asymmetric pinch conditions abstract in this paper we give an example of an asymmetric convex compact hypersurface possessing precisely n brake orbits for h c 1 r 2 n r satisfying h p q h p q for all p q r n r n we prove multiplicity result of the brake orbits on h 1 1 pinched by not necessarily symmetric hypersurfaces

the fadell rabinowitz index and multiplicity of non contractible closed geodesics on finsler rpn abstract in this paper we prove that for every irreversible finsler n dimensional real projective space r p n f with reversibility and flag curvature k satisfying 16 9 1 2 k 1 with 3 there exist at least n 1 non contractible closed geodesics in addition if the metric f is bumpy with 64 25 1 2 k 1 and 5 3 then there exist at least 2 n 1 2 non contractible closed geodesics which is the optimal lower bound due to katok s example the main ingredients of the proofs are the fadell rabinowitz index theory of non contractible closed geodesics on r p n f and the s 1 equivariant poincare series of the non contractible component of the free loop space on r p n

cayley s theorem and its application in the theory of vector pade approximants abstract le a be a matrix of even dimension which is anti symmetric after deletion of its r th row and column and let r c be the anti symmetric matrices formed by modifying the r th row and column of a respectively in this case cayley s 1857 theorem states that det a pf r pf c where pf r denotes the pfaffian of r a consequence of this theorem is an explicit factorisation of the standard determinantal representation of the denominator polynomial of a vector pade approximant we give a succinct modern proof of cayley s theorem then we prove a novel vector inequality arising from investigation of one such pfaffian and conjecture that all such pfaffians are nonnegative

monte carlo simulation of hard hyperspheres in six seven and eight dimensions for low to moderate densities the pair correlation function of hard hyperspheres in six seven and eight dimensions is obtained from monte carlo simulations the value of the pair correlation function at contact is compared with the results from molecular dynamics calculations and a variety of theoretical approaches remarkably good agreement is found with the simple closed form equations of y song e a mason and r m stratt j phys chem 93 6916 6919 1989 the monte carlo results for the equation of state are compared with the theoretical expressions of m baus and j l colot phys rev a 36 3912 1987 m luban and j p j michels phys rev a 41 6796 1990 and high order virial expansions in addition in seven dimensions comparisons are made with the exact py solution provided by m robles m l de haro and a santos j chem phys 120 9113 2004 very good agreement was observed between theory and computer simulation in all dimensions

problems and progress in vector pade approximation abstract some open problems in vector pade approximation are stated and some recent de montessus type theorems governing convergence of rows of the vector pade table are contrasted weshow how these results indicate when it is more appropriate to use generalised inverse vector pade approximants or their hybridised form we show how a straightforward analogue of the berlekamp massey algorithm may be used to calculate generalised inverse vector pade approximants this algorithm is applied to the derivation of a new low order hybrid vector approximant related results include the case of a row convergence theorem for a complex valued power series using a clifford inverse instead of the moore penrose inverse

on the normal exponential map in singular conformal metrics abstract brake orbits and homoclinics of autonomous dynamical systems correspond via maupertuis principle to geodesics in riemannian manifolds endowed with a metric which is singular on the boundary jacobi metric motivated by the classical yet still intriguing in many aspects problem of establishing multiplicity results for brake orbits and homoclinics as done in giambo et al 2005 2010 2011 and by the development of a morse theory in giambo et al 2014 for geodesics in such kind of metric in this paper we study the related normal exponential map from a global perspective

subharmonics for convex nonautonomous hamiltonian systems on etudie des solutions periodiques du systeme hamiltonien jx h t x ou j est la matrice symplectique standard et h c 2 r r 2n r est t periodique en la premiere variable pour tout t x h t x note le gradient partiel par rapport a la seconde variable

on critical point theory for indefinite functionals in the presence of symmetries we consider functionals which are not bounded from above or from below even modulo compact perturbations and which exhibit certain symmetries with respect to the action of a compact lie group we develop a method which permits us to prove the existence of multiple critical points for such functionals the proofs are carried out directly in an infinite dimensional hilbert space and they are based on minimax arguments the applications given here are to hamiltonian systems of ordinary differential equations where the existence of multiple time periodic solutions is established for several classes of hamiltonians symmetry properties of these hamiltonians such as time translation invariancy or evenness are exploited introduction many variational problems which arise from physics or mathematical physics are indefinite in the sense that the functionals involved are not bounded from below or from above however some of these functionals defined in an appropriate function space are semidefinite in the sense that they are bounded from below or from above if perturbed with a weakly continuous functional this paper deals with functionals which are not semidefinite usually problems involving indefinite functionals are more difficult to handle and only very recently a method has been developed which permits us to treat such problems directly in an infinite dimensional function space 7 in 7 some theorems have been proved which establish the existence of at least one nontrivial critical point for such functionals in many physical situations there are problems which have symmetries with respect to the action of some lie group in this case we expect the existence of many critical points this has been established for semidefinite functionals cf e g 8 and 3 for even functionals 9 for a zp action with p prime numbers 15 16 10 and 6 for an s action in this paper we develop a method which allows us to estimate the number of critical points of indefinite functionals in the presence of symmetries more precisely received by the editors july 16 1980 and in revised form june 26 1981 1980 mathematics subject classification primary 58e05 70h05 secondary 34c25

existence of orthogonal geodesic chords on riemannian manifolds with concave boundary and homeomorphic to the n dimensional disk abstract in this paper we give a proof of the existence of an orthogonal geodesic chord on a riemannian manifold homeomorphic to a closed disk and with concave boundary this kind of study is motivated by the link proved in giambo et al 2005 8 of the multiplicity problem with the famous seifert conjecture formulated in seifert 1948 1 about multiple brake orbits for a class of hamiltonian systems at a fixed energy level

closed characteristics on compact convex hypersurfaces in r 2n for any given compact c 2 hypersurface in r 2n bounding a strictly convex set with nonempty interior in this paper an invariant n is defined and satisfies n n 2 1 where a denotes the greatest integer which is not greater than a r the following results are proved in this paper there always exist at least n geometrically distinct closed characteristics on if all the geometrically distinct closed characteristics on are nondegenerate then n n if the total number of geometrically distinct closed characteristics on is finite there exists at least an elliptic one among them and there exist at least n 1 of them possessing irrational mean indices if this total number is at most 2 n 2 there exist at least two elliptic ones among them

on a theorem by ekeland and lasry concerning the number of periodic hamiltonian trajectories this note deals with the existence of iz distinct modes of vibration for hamihonian systems with n degrees of freedom on a prescribed energy surface this problem has been studied in a recent remarkable paper by ekeland and lasry 5 who have given an important contribution to the complete extension in the large of the local results of liapunov ri weinstein 111 and moser s the purpose of the present paper is to give a new proof of the result of 5 jointly with a slight improvement

irrationally elliptic closed characteristics on compact convex hypersurfaces in r6 abstract in this paper let r 6 be a compact convex hypersurface which carries exactly three geometrically distinct closed characteristics we prove that at least two of them must be irrationally elliptic

multiple brake orbits in bounded convex symmetric domains abstract in this paper we prove that there exist at least two geometrically distinct brake orbits in every bounded convex symmetric domain in r n for n 2

existence of multiple periodic orbits of hamiltonian systems on positive type hypersurfaces in r2n abstract this paper deals with the fixed energy problem of hamiltonian systems in r 2n the main result is an existence theorem of multiple periodic orbits for hamiltonian vector fields on a class of contact type but not necessarily star shaped hypersurfaces this is the first multiplicity result for hypersurfaces that are more general than star shaped ones the main result is achieved by using critical point theory for a special hamiltonian function and central gravity of the proof relies on a delicate construction of such hamiltonian function

periodic solutions with prescribed minimal period for convex autonomous hamiltonian systems clarke has shown that the problem of findingt periodic solutions for a convex hamiltonian system is equivalent to the problem of finding critical points to a certain functional dual to the classical action functional in this paper we relate the morse index of the critical point to the minimal period of the correspondingt periodic solution in particular we show that if the critical point is obtained by the ambrosetti rabinowitz mountain pass theorem the corresponding solution has minimal periodt that is it cannot bet k periodic withk integer k 2 as a consequence we prove that if the hamiltonian is flat near an equilibrium and superquadratic near infinity then for anyt 0 the corresponding hamiltonian system has a periodic solution with minimal periodt

functions on the sphere with critical points in pairs and orthogonal geodesic chords abstract using an estimate on the number of critical points for a morse even function on the sphere s m m 1 we prove a multiplicity result for orthogonal geodesic chords in riemannian manifolds with boundary that are diffeomorphic to euclidean balls this yields also a multiplicity result for brake orbits in a potential well

an index theory and existence of multiple brake orbits for star shaped hamiltonian systems soit h r 2n r une fonction continument differentiable et j o i ou i est la matrice identite n n on considere le systeme hamiltonien x jh x on etudie l existence de solutions periodiques sur une hypersurface compacte donnee h 1 1

a new index theory for linear self adjoint operator equations and its applications abstract we develop an index theory for linear self adjoint operator equation with the linear self adjoint operator having no compact resolvent as applications we consider the existence and multiplicity of periodic solutions of wave equations and beam equations

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

solutions of minimal period for a class of nonconvex hamiltonian systems and applications to the fixed energy problem on considere le systeme hamiltonien jz h z ou j x y y x x y r n r n h est non convexe a un bon comportement superquadratique et satisfait une condition simple reliant ses coefficients de superquadraticite et l exposant dans ce cas on demontre que pour t 0 l existence de solutions pour le systeme hamiltonien de periode minimale t

existence of multiple normal mode trajectories on convex energy surfaces of even classical hamiltonian systems hamiltonian systems of n degrees of freedom for which the hamiltonian is a function that is even both in its joint n coordinate variables as well as in its joint n momentum variables are discussed for such systems the number of distinct trajectories which correspond to particular periodic solutions normal modes with the same energy is investigated to that end a constrained dual action principle is introduced applying min max methods to this variational problem several results are obtained among which the existence of at least n distinct trajectories if specific conditions are satisfied

resonance identity for symmetric closed characteristics on symmetric convex hamiltonian energy hypersurfaces and its applications in this paper we establish a new resonance identity for symmetric closed characteristics on symmetric compact convex hypersurface in r2n when there exist only finitely many geometrically distinct symmetric closed characteristics as its applications some interesting results about the stability and multiplicity of symmetric closed characteristics are obtained and also we prove that if is c generic it carries infinitely many symmetric closed characteristics

partial skew orthogonal polynomials and related integrable lattices with pfaffian tau functions skew orthogonal polynomials sops arise in the study of the n point distribution function for orthogonal and symplectic random matrix ensembles motivated by the average of characteristic polynomials of the bures random matrix ensemble studied in forrester and kieburg commun math phys 342 1 151 187 2016 we propose the concept of partial skew orthogonal polynomials psops as a modification of the sops and then the psops with a variety of special skew symmetric kernels and weight functions are addressed by considering appropriate deformations of the weight functions we derive nine integrable lattices in different dimensions as a consequence the tau functions for these systems are shown to be expressed in terms of pfaffians and the wave vectors psops in fact the tau functions also admit the multiple integral representations among these integrable lattices some of them are known while the others are novel to the best of our knowledge in particular one integrable lattice is related to the partition function of the bures ensemble besides we derive a discrete integrable lattice which can be used to compute certain vector pade approximants this yields the first example regarding the connection between integrable lattices and generalised inverse vector valued pade approximants about which hietarinta joshi and nijhoff pointed out that this field remains largely to be explored in the recent monograph hietarinta et al in discrete systems and integrability vol 54 cambridge university press cambridge 2016 section 4 4

on the covering of a hill s region by solutions in systems with gyroscopic forces abstract consider a lagrangian system with the lagrangian containing terms linear in velocity by analogy with the systems in celestial mechanics we call a bounded connected component of the possible motion area of such a system a hill s region suppose that the energy level is fixed and the corresponding hill s region is compact we present sufficient conditions under which any point in the hill s region can be connected with its boundary by a solution with the given energy the result is illustrated by examples from mechanics

a twist condition and multiple solutions of unbounded self adjoint operator equation with symmetries abstract by using the index theory for unbounded self adjoint operator equations and the symmetric mountain pass theorem we investigate the existence of multiple solutions for nonlinear operator equations with twist conditions we prove an abstract theorem and give some applications to first order hamiltonian systems with sturm liouville boundary conditions and delay differential equations

periodic solutions on hypersurfaces and a result by c viterbo on considere un champ vectoriel hamiltonien x j h x x h x sur x r 2n h etant une fonction lisse dont le gradient h est defini par rapport a la metrique euclidienne on cherche des solutions periodiques sur une surface d energie donnee s x r 2n h x const supposee reguliere

index iteration theories for periodic orbits old and new abstract in this paper we give a survey of the index iteration theories developed for periodic solution orbits of hamiltonian systems in treating various problems from 1950s up to now including some recent developments and some of their applications to periodic solution problems

a twist condition and periodic solutions of hamiltonian systems abstract in this paper we investigate existence of nontrivial periodic solutions to the hamiltonian system hs j z h t z z r 2 n under a general twist condition for the hamiltonian function in terms of the difference of the conley zehnder index at the origin and at infinity we establish existence of nontrivial periodic solutions compared with the existing work in the literature our results do not require the hamiltonian function to have linearization at infinity our results allow interactions at infinity between the hamiltonian and the linear spectra the general twist condition raised here seems to resemble more the spirit of poincare s last geometric theorem

periodic orbits of hamiltonian systems on symmetric positive type hypersurfaces this paper discusses the existence and multiplicity of periodic orbits of hamiltonian systems on symmetric positive type hypersurfaces we prove that each such energy hypersurface carries at least one symmetric periodic orbit under some suitable pinching conditions we also get an existence result of multiple symmetric periodic orbits

lusternik schnirelmann theory and closed reeb orbits we develop a variant of lusternik schnirelmann theory for the shift operator in equivariant floer and symplectic homology our key result is that the spectral invariants are strictly decreasing under the action of the shift operator when periodic orbits are isolated as an application we prove new multiplicity results for simple closed reeb orbits on the standard contact sphere the unit cotangent bundle to the sphere and some other contact manifolds we also show that the lower conley zehnder index enjoys a certain recurrence property and revisit and reprove from a different perspective a variant of the common jump theorem of long and zhu this is the second combinatorial ingredient in the proof of the multiplicity results

convex hamiltonian energy surfaces and their periodic trajectories in this paper we introduce symplectic invariants for convex hamiltonian energy surfaces and their periodic trajectories and show that these quentities satisfy several nontrivial relations in particular we show that they can be used to prove multiplicity results for the number of periodic trajectories

generalized inverse matrix pade approximation on the basis of scalar products a new type of generalized matrix inverse is used to define the generalized inverse matrix pade approximants gmpa gmpa is introduced on the basis of scalar product of matrices with the form of matrix numerator and scalar denominator it is different from the existing matrix pade approximants in that it does not need multiplication of matrices in the construction process some algebraic properties are discussed the representations of gmpa are provided with the following three forms i the explicit determinantal formulas for the denominator scalar polynomials and the numerator matrix polynomials ii e algorithm expression iii thiele type continued fraction expression the equivalence relations above three representations are proposed

a z p borsuk ulam theorem and index theory with a multiplicity result in partial differential equations on demontre un theoreme de borsuk ulam z p generalise c est le resultat topologique essentiel pour developper un theoreme d indice z p on demontre un resultat de multiplicite pour un systeme d equations aux derivees partielles elliptiques non lineaires

automatic renal cortex segmentation using implicit shape registration and novel multiple surfaces graph search in this paper we present an automatic renal cortex segmentation approach using the implicit shape registration and novel multiple surfaces graph search the proposed approach is based on a hierarchy system first the whole kidney is roughly initialized using an implicit shape registration method with the shapes embedded in the space of euclidean distance functions second the outer and inner surfaces of renal cortex are extracted utilizing multiple surfaces graph searching which is extended to allow for varying sampling distances and physical constraints to better separate the renal cortex and renal column third a renal cortex refining procedure is applied to detect and reduce incorrect segmentation pixels around the renal pelvis further improving the segmentation accuracy the method was evaluated on 17 clinical computed tomography scans using the leave one out strategy with five metrics dice similarity coefficient dsc volumetric overlap error oe signed relative volume difference svd average symmetric surface distance davg and average symmetric rms surface distance drms the experimental results of dsc oe svd davg and drms were 90 50 1 19 4 38 3 93 2 37 1 72 0 14 mm 0 09 mm and 0 80 mm 0 64 mm respectively the results showed the feasibility efficiency and robustness of the proposed method

resonance identities for closed characteristics on compact star shaped hypersurfaces in r2n resonance relations among periodic orbits on given energy hypersurfaces are very important for getting deeper understanding of the dynamics of the corresponding hamiltonian systems in this paper we establish two new resonance identities for closed characteristics on every compact star shaped hypersurface in r2n when the number of geometrically distinct closed characteristics on is finite which extend those identities established by c viterbo in 1989 for star shaped hypersurfaces assuming in addition that all the closed characteristics and their iterates are non degenerate and that by w wang x hu and y long in 2007 for strictly convex hypersurfaces in r2n

seifert conjecture in the even convex case in this paper we prove that there exist at least n geometrically distinct brake orbits on every c2 compact convex symmetric hypersurface in 2n satisfying the reversible condition n with n diag in in as a consequence we show that if the hamiltonian function is convex and even then seifert conjecture of 1948 on the multiplicity of brake orbits holds for any positive integern 2014 wiley periodicals inc

multiplicity of characteristics with lagrangian boundary values on symmetric star shaped hypersurfaces abstract in this paper the multiplicity of lagrangian orbits on c 2 smooth compact symmetric star shaped hypersurfaces with respect to the origin in r 2 n is studied these lagrangian orbits begin from one lagrangian subspace and end on another an infinitely many existence result is proved via z 2 index theory this is a multiplicity result about the arnold chord conjecture in some sense and is a generalization of the problem about the multiplicity of lagrangian orbits beginning from and ending on the same lagrangian subspace which was considered in the authors previous paper f guo c liu multiplicity of lagrangian orbits on symmetric star shaped hypersurfaces nonlinear anal 69 4 2008 1425 1436

iteration theory of l index and multiplicity of brake orbits abstract in this paper we first establish the bott type iteration formulas and some abstract precise iteration formulas of the maslov type index theory associated with a lagrangian subspace for symplectic paths as an application we prove that there exist at least n 2 1 geometrically distinct brake orbits on every c 2 compact convex symmetric hypersurface in r 2 n satisfying the reversible condition n furthermore if all brake orbits on this hypersurface are nondegenerate then there are at least n geometrically distinct brake orbits on it as a consequence we show that there exist at least n 2 1 geometrically distinct brake orbits in every bounded convex symmetric domain in r n furthermore if all brake orbits in this domain are nondegenerate then there are at least n geometrically distinct brake orbits in it in the symmetric case we give a positive answer to the seifert conjecture of 1948 under a generic condition

analytical mini max methods for hamiltonian brake orbits of prescribed energy on considere des caracterisations explicites de solutions periodiques de systemes hamiltoniens autonomes d ordre 2 de la forme q v q q t r n ou le potentiel v satisfait les conditions suivantes v c 2 r n v x v o 0 v est strictement convexe sur r n

examples with minimal number of brake orbits and homoclinics in annular potential regions abstract we use a geometric construction to exhibit examples of autonomous lagrangian systems admitting exactly two homoclinics emanating from a nondegenerate maximum of the potential energy and reaching a regular level of the potential having the same value of the maximum point similarly we show examples of hamiltonian systems that admit exactly two brake orbits in an annular potential region connecting the two connected components of the boundary of the potential well these examples show that the estimates proven in 2 are sharp

subharmonic solutions and morse theory abstract a forced oscillation problem for a hamiltonian equation on a torus is studied if the dimension of the torus is equal to 2n and if the period of the time dependent hamiltonian equation is equal to 1 there are at least 2n 1 periodic solutions having period 1 in this paper it is shown that under an additional necessary nondegeneracy condition such an equation possesses a periodic solution having minimal period t for every sufficiently large prime number t the proof uses the classical variational approach it is based on the morse theory for periodic solution to its morse index and on an iteration formula for the winding number originator supplied keywords included hamiltonian systems periodic solutions variational principles morse type index theory winding number of a periodic solution and reprints

brake type closed characteristics on reversible compact convex hypersurfaces in r2n abstract in this paper let be a c 3 compact convex in r 2 n satisfying the reversible condition n with n diag i n i n we prove that if there are exactly n geometrically distinct closed characteristics on and all of them are nondegenerate then all of them must be brake orbits up to a suitable translation of time moreover for n 2 or 3 we prove that if there are exactly n geometrically distinct closed characteristics on then all of them must be brake orbits up to a suitable translation of time

morse type index theory for flows and periodic solutions for hamiltonian equations an index theory for flows is presented which extends the classical morse theory for gradient flows on compact manifolds the theory is used to prove a morse type existence statement for periodic solutions of a time dependent periodic in time and asymptotically linear hamiltonian equation

existence of multiple periodic orbits on star shaped hamiltonian surfaces consider the hamiltonian system hs i 1 n here h c2 2n in this paper we investigate the existence of periodic orbits of hs on a given energy surface z 2n h z c c o is a constant the surface is required to verify certain geometric assumptions bounds a star shaped compact region and for some ellipsoid 2n o o depending in an explicit fashion on the lengths of the main axes of and one other geometrical parameter of such that if furthermore 2 2 1 then hs has at least n distinct geometric orbits on this result is shown to extend and unify several earlier works on this subject among them works by weinstein rabinowitz ekeland lasry and ekeland in proving this result we construct index theories for an s1 action from which we derive abstract critical point theorems for s1 invariant functionals we also derive an estimate for the minimal period of solutions to differential equatious

from matrix to vector pade approximants abstract reliable modified euclidean and kronecker algorithms for real and complex vector valued power series are constructed by exploiting an isomorphism between vectors and matrices this is done using mcleod s 1971 clifford algebra representation which preserves the moore penrose inverse this approach required new proofs of wynn s and cordellier s identities which do not involve the use of determinants