A construction of realizations of perturbations of Poincaré maps
A functional analysis approach to Arnold diffusion
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results.
A KAM phenomenon for singular holomorphic vector fields
Let X be a germ of holomorphic vector field at the origin of Cn and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are biholomorphic to the intersection...
A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems.
A new method for measuring the splitting of invariant manifolds
Abelian integrals for quadratic vector fields.
Action minimizing invariant measures for positive definite Lagrangian systems.
Approximation of invariant surfaces by periodic orbits in high-dimensional maps: Some rigorous results.
Asymptotic stability for perturbed hamiltonian systems, II
Asymptotic stability of dynamical systems with multiplicative perturbations
Bifurcation d'orbites homoclines pour les systèmes hamiltoniens
Bifurcation of periodic and chaotic solutions in discontinuous systems
Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given...
Bohr–Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.
Branching of periodic orbits from Kukles isochrones.
Changing rotation intervals of endomorphisms of the circle.
Classical integrable mechanical systems and their integrable perturbations.
Correction to: Connecting invariant manifolds and the solution of the stability and -stability conjectures for flows.
Dédoublement de courbes invariantes sur le cylindre : petits diviseurs
Dérivabilité du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes à coefficients positifs