‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...

The aim of this note is to present an introduction to Birkhoff normal form and to its use for the study of the dynamics of a Hamiltonian system close to an elliptic equilibrium point. Recall that Birkhoff’s theorem ensures the existence of a canonical transformation putting a Hamiltonian system in normal form up to a remainder of a given order. The dynamics of the system in normal form depends ...

We construct a Hamiltonian suspension for a given symplectomorphism which is the perturbation of a Poincaré map. This is especially useful for the conversion of perturbative results between symplectomorphisms and Hamiltonian flows in any dimension 2d. As an application, using known properties of area-preserving maps, we prove that for any Hamiltonian defined on a symplectic 4-manifold M and any...

We consider solutions of the matrix KP hierarchy that are elliptic functions first hierarchical time $t_1=x$. It is known poles $x_i$ and residues at $\rho_i^{\alpha \beta}=a_i^{\alpha}b_i^{\beta}$ such as $t_2$ move particles spin generalization Calogero-Moser model (elliptic Gibbons-Hermsen model). In this paper we establish correspondence with for whole hierarchy. Namely, show dynamics respe...

It is known that the trigonometric Calogero-Sutherland model is obtained by the trigonometric limit (τ → √ −1∞) of the elliptic CalogeroMoser model, where (1, τ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero-Sutherland model, if exp(2π √ −1τ) is small enough then there exist square-integrable eig...

In this article, we consider linearly stable elliptic fixed points (equilibrium) for a symplectic vector field and we prove generic results of super-exponential stability for nearby solutions. We will focus on the neighbourhood of elliptic fixed points but the case of linearly stable isotropic reducible invariant tori in an Hamiltonian system should be similar. More specifically, Morbidelli and...

We prove a conjecture by N.N. Nekhoroshev about the long{time stability of elliptic equilibria of Hamiltonian systems, without any Diophantine condition on the frequencies. Higher order terms of the Hamiltonian are used to provide convexity. The singularity of the action{angle coordinates at the origin is overcome by working in cartesian coordinates.