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 ?
Periodic orbits close to elliptic tori and applications to the three-body problem
We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses...
Periodic solutions of second order hamiltonian systems bifurcating from infinity
Perturbation by analytic discs along maximal real submanifolds of CN.
Perturbation results for a class of singular Hamiltonian systems
The existence of solutions with prescribed period for a class of Hamiltonian systems with a Keplerian singularity is discussed.
Perturbation theory and discrete Hamiltonian dynamics.
Perturbations of stable invariant tori for hamiltonian systems
Perturbations of the spherical pendulum and Abelian integrals.
Perturbative computation of analytic invariants of resonant diffeomorphisms of
Perturbazioni periodiche di equazioni differenziali ordinarie su varietà differenziabili
Poincaré-Melnikov theory for n-dimensional diffeomorphisms
We consider perturbations of n-dimensional maps having homo-heteroclinic connections of compact normally hyperbolic invariant manifolds. We justify the applicability of the Poincaré-Melnikov method by following a geometric approach. Several examples are included.
Propriétés générales des applications déviant la verticale
Randomly connected dynamical systems - asymptotic stability
We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.