Amadeu Delshams

A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model

Introduction Heuristic discussion of the mechanism A simple model Statement of rigorous results Notation and definitions, resonances Geometric features of the unperturbed problem Persistence of the normally hyperbolic invariant manifold and its stable and unstable manifolds The dynamics in

A Geometric Approach to the Existence of Orbits with Unbounded Energy in Generic Periodic Perturbations by a Potential of Generic Geodesic Flows of ?2}

\tilde \Lambda_{\varepsilon}

KAM theory and a partial justification of Greene's criterion for nontwist maps

The scattering map Existence of transition chains Orbits shadowing the transition chains and proof of Theorem 4.1 Conclusions and remarks An example Acknowledgments Bibliography.

Splitting Potential and the Poincaré-Melnikov Method for Whiskered Tori in Hamiltonian Systems

Abstract:We give a proof based in geometric perturbation theory of a result proved by J. N. Mather using variational methods. Namely, the existence of orbits with unbounded energy in perturbations of a generic geodesic flow in ?2 by a generic periodic potential.

Poincaré - Melnikov - Arnold method for analytic planar maps

We consider perturbations of integrable, area preserving nontwist maps of the annulus (those are maps in which the twist condition changes sign). These maps appear in a variety of applications, notably transport in atmospheric Rossby waves. We show in suitable two-parameter families the persistence of critical circles (invariant circles whose rotation number is the maximum of all the rotation numbers of points in the map) with Diophantine rotation number. The parameter values with critical circles of frequency

Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

\omega_0

Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps*

lie on a one-dimensional analytic curve.Furthermore, we show a partial justification of Greenes criterion: If analytic critical curves with Diophantine rotation number

Geometric approaches to the problem of instability in Hamiltonian systems. An informal presentation

\omega_0

A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results

exist, the residue of periodic orbits (that is, one fourth of the trace of the derivative of the return map minus 2) with rotation number converging to

Homoclinic billiard orbits inside symmetrically perturbed ellipsoids

\omega_0