On a conjecture for the critical behaviour of KAM tori.
On classical intrinsically resonant formal perturbation theory
On Elliptic Lower Dimensional Tori in Hamiltonian Systems.
On persistence of invariant tori and a theorem by Nekhoroshev.
On the C⁰-closing lemma
A proof of the C⁰-closing lemma for noninvertible discrete dynamical systems and its extension to the noncompact case are presented.
On the existence of homoclinic points
On the growth of averaged Weyl sums for rigid rotations
On the KAM - Theory Conditions for the Kirchhoff Top
* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.In this paper the classical Kirchhoff case of motion of a rigid body in an infinite ideal fluid is considered. Then for the corresponding Hamiltonian system on the zero integral level, the KAM theory conditions are checked. In contrast to the known similar results, there exists a curve in the bifurcation diagram along which the Kolmogorov’s condition vanishes for certain values of the parameters.
Optimalité systolique infinitésimale de l’oscillateur harmonique
Nous étudions les aspects infinitésimaux du problème suivant. Soit un hamiltonien de dont la surface d’énergie borde un domaine compact et étoilé de volume identique à celui de la boule unité de . La surface d’énergie contient-elle une orbite périodique du système hamiltoniendont l’action soit au plus ?