Invariant varieties of periodic points for the discrete Euler top.
We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...
In this paper, we consider the natural complex Hamiltonian systems with homogeneous potential , , of degree . The known results of Morales and Ramis give necessary conditions for the complete integrability of such systems. These conditions are expressed in terms of the eigenvalues of the Hessian matrix calculated at a non-zero point , such that . The main aim of this paper is to show that there are other obstructions for the integrability which appear if the matrix is not diagonalizable....
This talk is concerned with the Kolmogorov-Arnold-Moser (KAM) theorem in Gevrey classes for analytic hamiltonians, the effective stability around the corresponding KAM tori, and the semi-classical asymptotics for Schrödinger operators with exponentially small error terms. Given a real analytic Hamiltonian close to a completely integrable one and a suitable Cantor set defined by a Diophantine condition, we find a family , of KAM invariant tori of with frequencies which is Gevrey smooth with...
A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two.
We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.
Nous nous proposons de réenvisager sous un éclairage très particulier la naissance bien connue de la dynamique classique à travers les travaux de Galilée, Huygens et Newton. Il s’agit de montrer que si les trajectoires les plus générales décrites par des corps pesants sont les coniques d’Apollonius, c’est parce que le problème de l’établissement des trajectoires a été prémathématisé par des principes généraux sous-jacents à l’étude du lien entre causes et effets. L’introduction de ces présupposés...
Communément associée au nom de l’ingénieur allemand Carl Culmann, la statique graphique a failli, en fait, naître à plusieurs reprises en France. En avance dans un premier temps, les savants et ingénieurs français vont pourtant « rater » l’occasion de devenir les véritables créateurs de cette méthode de calcul graphique. Élaborée pour l’essentiel en dehors de l’Hexagone, la statique graphique va se diffuser en France durant le dernier tiers du xixe siècle comme un produit d’importation et avec un...