homoclinic solutions for singular hamiltonian systems without the strong force condition abstract we consider the existence of homoclinic orbits at the origin of a hamiltonian system q v q 0 in r n n 3 where v has a strict global maximum at q 0 and a singularity at a point e 0 namely v q as q e we establish via variational methods the existence of a generalized homoclinic orbit q that may enter the singularity e without assuming the strong force condition of gordon moreover when v 1 q e 0 2 near e we give a bound for the number of collisions of q based on the morse index of approximated solutions as a consequence we obtain that q is classical non collision orbit for 1 2 and enters the singularity e at most one time in r if 0 1

unitary representations of affine hecke algebras related to macdonald spherical functions abstract for any reduced crystallographic root system we introduce a unitary representation of the extended affine hecke algebra given by discrete difference reflection operators acting in a hilbert space of complex functions on the weight lattice it is shown that the action of the center under this representation is diagonal on the basis of macdonald spherical functions as an application we compute an explicit pieri formula for these spherical functions

a noncollision periodic solution for n body problems using variational minimization methods we prove the existence of one noncollision periodic solution for n body type problems whose potentials are pinched between two homogeneous potentials in rk k 2

multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces abstract the existence of multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces is discussed in this paper our nonlinearity may be singular in its dependent variable and our analysis relies on a nonlinear alternative of leray schauder type and on a fixed point theorem in cones

a deformation of affine hecke algebra and integrable stochastic particle system we introduce a deformation of the affine hecke algebra of type which describes the commutation relations of the divided difference operators found by lascoux and schutzenberger and the multiplication operators making use of its representation we construct an integrable stochastic particle system it is a generalization of the q boson system due to sasamoto and wadati we also construct eigenfunctions of its generator using the propagation operator as a result we get the same eigenfunctions for the boson process obtained by povolotsky

exact results for one dimensional totally asymmetric diffusion models several types of totally asymmetric diffusion models with and without exclusion are considered for some models conditional probabilities of finding n particles on lattice sites at time t with initial occupation at time t 0 are expressed in a determinant form on the other hand the q boson totally asymmetric diffusion model is introduced which interpolates the free boson model and the model with exclusion like interaction the effects of the interaction are compared for the case of two particle diffusion

periodic solutions of a class of singular hamiltonian systems soit r n 0 n n n 3 et soit v c 1 rx r on etudie l existence des solutions periodiques t u t avec une periode prescrite du systeme suivant de n equations differentielles d ordre 2 u v t u

a new generalisation of macdonald polynomials we introduce a new family of symmetric multivariate polynomials whose coefficients are meromorphic functions of two parameters q t and polynomial in a further two parameters u v we evaluate these polynomials explicitly as a matrix product at u v 0 they reduce to macdonald polynomials while at q 0 u v s they recover a family of inhomogeneous symmetric functions originally introduced by borodin

homoclinic orbits for second order hamiltonian systems possessing superquadratic potentials received by the editors november 27 1990 1991 mathematics subject classification primary 34c99 58e99 58f99 the first author was supported by ministero p i gruppo 40 calcolo delle variazioni the second author s research was sponsored in part by the u s army research office under contract daal03 87 k 0043 the national science foundation under grant mcs 8110556 and the office of naval research under grant n00014 88 ko134 any reproduction for the purpose of the united states govemment is permitted

periodic solutions of a class of hamiltonian systems with singularities this paper deals with a class of time periodic hamiltonian systems obtained by a time dependent perturbation from an autonomous system with a singularity at q 0 in configuration space it is shown that t being the period of the perturbation nondegenerate families of t periodic orbits in the unperturbed problem branch off into a certain number of t periodic orbits for the perturbed problem

spectral theory for interacting particle systems solvable by coordinate bethe ansatz we develop spectral theory for the q hahn stochastic particle system introduced recently by povolotsky that is we establish a plancherel type isomorphism result that implies completeness and biorthogonality statements for the bethe ansatz eigenfunctions of the system owing to a markov duality with the q hahn tasep a discrete time generalization of tasep with particles jump distribution being the orthogonality weight for the classical q hahn orthogonal polynomials we write down moment formulas that characterize the fixed time distribution of the q hahn tasep with general initial data the bethe ansatz eigenfunctions of the q hahn system degenerate into eigenfunctions of other not necessarily stochastic interacting particle systems solvable by the coordinate bethe ansatz this includes the asep the asymmetric six vertex model and the heisenberg xxz spin chain all models are on the infinite lattice in this way each of the latter systems possesses a spectral theory too in particular biorthogonality of the asep eigenfunctions which follows from the corresponding q hahn statement implies symmetrization identities of tracy and widom for asep with either step or step bernoulli initial configuration as corollaries another degeneration takes the q hahn system to the q boson particle system dual to q tasep studied in detail in our previous paper 2013 thus at the spectral theory level we unify two discrete space regularizations of the kardar parisi zhang equation stochastic heat equation namely q tasep and asep

homoclinic orbits for a class of hamiltonian systems consider the second order hamiltonian system where q n and v c 1 n is t periodic in t suppose v q t 0 0 0 is a local maximum for v t and v t x x under these and some additional technical assumptions we prove that hs has a homoclinic orbit q emanating from 0 the orbit q is obtained as the limit as k of 2 kt periodic solutions i e subharmonics q k of hs the subharmonics q k are obtained in turn via the mountain pass theorem

motion field and optical flow qualitative properties it is shown that the motion field the 2 d vector field which is the perspective projection on the image plane of the 3 d velocity field of a moving scene and the optical flow defined as the estimate of the motion field which can be derived from the first order variation of the image brightness pattern are in general different unless special conditions are satisfied therefore dense optical flow is often ill suited for computing structure from motion and for reconstructing the 3 d velocity field by algorithms which require a locally accurate estimate of the motion field a different use of the optical flow is suggested it is shown that the smoothed optical flow and the motion field can be interpreted as vector fields tangent to flows of planar dynamical systems stable qualitative properties of the motion field which give useful informations about the 3 d velocity field and the 3 d structure of the scene usually can be obtained from the optical flow the idea is supported by results from the theory of structural stability of dynamical systems

on the existence of infinitely many periodic solutions to some problems of n body type we prove the existence of infinitely many periodic solutions with prescribed period to a class of problems of n body type

perturbation of hamiltonian systems with keplerian potentials on considere l existence des solutions periodiques pour une classe de systemes hamiltoniens obtenus comme des perturbations de l hamiltonien keplerien k p q 1 2 p 2 q 0

morse index and stability of elliptic lagrangian solutions in the planar three body problem abstract we illustrate a new way to study the stability problem in celestial mechanics in this paper using the variational nature of elliptic lagrangian solutions in the planar three body problem we study the relation between morse index and its stability via maslov type index theory of periodic solutions of hamiltonian system for elliptic lagrangian solutions we get an estimate of the algebraic multiplicity of unit eigenvalues of its monodromy matrix in terms of the morse index which is the key to understand the stability problem as a special case we provide a criterion to spectral stability of relative equilibrium

combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice we introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in a finite lattice we introduce the l operator related to the uq sl2 r matrix and construct the wavefunctions and their duals we prove the exact correspondence between the wavefunctions and symmetric polynomials which is a quantum group deformation of the grothendieck polynomials this is proved by combining the matrix product method and an analysis on the domain wall boundary partition functions as applications of the correspondence between the wavefunctions and symmetric polynomials we derive several properties of the symmetric polynomials such as the determinant pairing formulas and the branching formulas by analyzing the domain wall boundary partition functions and the matrix elements of the b operators

on the integrability of zero range chipping models with factorized steady states the conditions of the integrability of general zero range chipping models with factorized steady states which were proposed in evans et al 2004 j phys a math gen 37 l275 are examined we find a three parametric family of hopping probabilities for the models solvable by the bethe ansatz which includes most of known integrable stochastic particle models as limiting cases the solution is based on the quantum binomial formula for two elements of an associative algebra obeying generic homogeneous quadratic relations which is proved as a byproduct we use the bethe ansatz to solve an eigenproblem for the transition matrix of the markov process on its basis we conjecture an integral formula for the green function of the evolution operator for the model on an infinite lattice and derive the bethe equations for the spectrum of the model on a ring

a relationship between the periodic and the dirichlet bvps of singular differential equations in this paper a relationship between the periodic and the dirichlet boundary value problems for second order ordinary differential equations with singularities is established this relationship may be useful in explaining the difference between the nonresonance of singular and nonsingular differential equations using this relationship we give in this paper an existence result of positive periodic solutions to singular differential equations when the singular forces satisfy some strong force condition at the singularity 0 and some linear growth condition at infinity

the g invariant implicit function theorem in infinite dimensions ii our basic theorem is a version of the implicit function theorem in the case of continuous groups of symmetries the result is sufficiently general to cover a great many applications it generalizes some earlier work of the author and corrects and improves some work of vanderbauwhede we also consider the breaking of symmetries problem and the variational case finally we apply our results to study the periodic solutions of an ordinary differential equation

self calibration of a moving camera from pointcorrespondences and fundamental matrices we address the problem of estimating three dimensional motion and structure from motion with an uncalibrated moving camera we show that point correspondences between three images and the fundamental matrices computed from these point correspondences are sufficient to recover the internal orientation of the camera its calibration the motion parameters and to compute coherent perspective projection matrices which enable us to reconstruct 3 d structure up to a similarity in contrast with other methods no calibration object with a known 3 d shape is needed and no limitations are put upon the unknown motions to be performed or the parameters to be recovered as long as they define a projective camera the theory of the method which is based on the constraint that the observed points are part of a static scene thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic is first detailed several algorithms are then presented and their performances compared by means of extensive simulations and illustrated by several experiments with real images

homoclinics and heteroclinics for a class of conservative singular hamiltonian systems abstract we consider an autonomous hamiltonian system u v u 0 where the potential v r 2 r has a strict global maximum at the origin and a singularity at some point 0 under some compactness conditions on v at infinity and around the singularity we study the existence of homoclinic orbits to 0 winding around we use a sufficient and in some sense necessary geometrical condition on v to prove the existence of infinitely many homoclinics each one being characterized by a distinct winding number around moreover under the condition there exists a minimal non contractible periodic orbit and we establish the existence of a heteroclinic orbit from 0 to this connecting orbit is obtained as the limit in the c 1 loc topology of a sequence of homoclinics with a winding number larger and larger

a minimax method for a class of hamiltonian systems with singular potentials abstract this paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of hamiltonian systems when a singular potential is present the singularity satisfies the strong force condition of gordon when milder singularities are permitted a notion of generalized t periodic solution is introduced and we get existence and multiplicity results for such solutions

on a class of singular second order hamiltonian systems with infinitely many homoclinic solutions abstract we show existence of infinitely many homoclinic orbits at the origin for a class of singular second order hamiltonian systems u v u t u 0 t we use variational methods under the assumption that v t u satisfies the so called strong force condition

c velocity a flow cumulating uncalibrated approach for 3d plane detection this paper deals with plane detection from a monocular image sequence without camera calibration or a priori knowledge about the egomotion within a framework of driver assistance applications it is assumed that the 3d scene is a set of 3d planes in this paper the vision process considers obstacles roads and buildings as planar structures these planes are detected by exploiting iso velocity curves after optical flow estimation a hough transform like frame called c velocity was designed this paper explains how this c velocity defined by analogy to the v disparity in stereovision can represent planes regardless of their orientation and how this representation facilitates plane extraction under a translational camera motion planar surfaces are transformed into specific parabolas of the c velocity space the error and robustness analysis of the proposed technique confirms that this cumulative approach is very efficient for making the detection more robust and coping with optical flow imprecision moreover the results suggest that the concept could be generalized to the detection of other parameterized surfaces than planes

collisionless periodic solutions to some three body problems we provide sufficient conditions for the existence of periodic solutions to some three body problems periodic solutions are found as minima of the associated action integral and are shown to be free of double and triple collisions

matrix product formula for u _ q a_ 2 1 zero range process the zero range processes introduced recently by mangazeev maruyama and the authors are integrable discrete and continuous time markov processes associated with the stochastic r matrix derived from the well known quantum r matrix by constructing a representation of the relevant zamolodchikov faddeev algebra we present for n 2 a matrix product formula for the steady state probabilities in terms of q boson operators

periodic solutions of prescribed energy for a class of hamiltonian systems with singular potentials abstract we study the existence of periodic solutions of prescribed energy for a class of hamiltonian systems with singular potentials we found periodic solutions lying between two prescribed spheres

symmetrically homoclinic orbits for symmetric hamiltonian systems in this paper we study the existence of symmetric homoclinic orbits for first order and second order hamiltonian systems with some symmetric hamiltonian functions

new periodic solutions for 2n body problems in r3 for newtonian 2n body problems with equal masses in r3 we prove the existence of new noncollision periodic solution such that 2n bodies move on two different closed curves

closed orbits of fixed energy for singular hamiltonian systems this paper deals with the existence of periodic solutions of q v q 0 such that 1 2 q 2 v q h where q r n h is a given number v c 2 r n 0 r has a singularity at x 0 and v denotes the gradient of v

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

multiple closed orbits of fixed energy forn body type problems with gravitational potentials abstract using the equivariant ljusternik schnirelmann theory and the estimates of the upper bound and lower bound of the critical values for the variational functional we obtain results in general concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planarn body type problems

geometric characterization for variational minimization solutions of the 3 body problem with fixed energy abstract in this paper for any given positive masses we prove that the constrained variational minimization solutions of the fixed energy or fixed mean potential energy problem for the 3 body type problems with homogeneous potentials in r 3 or r 2 are precisely the planar equilateral triangle circular solutions found by j lagrange in 1772

on a family of symmetric rational functions abstract this paper is about a family of symmetric rational functions that form a one parameter generalization of the classical hall littlewood polynomials we introduce two sets of skew and non skew functions that are akin to the p and q hall littlewood polynomials we establish a a combinatorial formula that represents our functions as partition functions for certain path ensembles in the square grid b symmetrization formulas for non skew functions c identities of cauchy and pieri type d explicit formulas for principal specializations e two types of orthogonality relations for non skew functions our construction is closely related to the half infinite volume finite magnon sector limit of the higher spin six vertex or xxz model with both sets of functions representing higher spin six vertex partition functions and or transfer matrices for certain domains

periodic solutions to some problems of n body type we prove the existence of at least one t periodic solution to a dynamical system of the type m i ddot u i sum limits j 1 j ne i n triangledown v ij u i u j text t 1 where the potentials v ij are t periodic in t and singular at the origin u i e r k i 1 n and k 3 we also provide estimates on the h 1 norm of this solution the proofs are based on a variant of the ljusternik schnirelman method the results here generalize to the n body problem some results obtained by bahri rabinowitz on the 3 body problem in 6