Poincaré's program for the global analysis of a dynamical system starts by considering
simple solutions, such as equilibria and periodic orbits, together with their corresponding …

In this paper, we present and illustrate a general methodology to apply KAM theory in
particular problems, based on an a posteriori approach. We focus on the existence of real …

When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, families
of unstable periodic orbits break up into whiskered tori, with most tori persisting into the …

In this paper we present an a-posteriori KAM theorem for the existence of an (n− d)-
parameter family of d-dimensional isotropic invariant tori with Diophantine frequency vector …

In this paper we present efficient algorithms for the computation of several invariant objects
for Hamiltonian dynamics. More precisely, we consider KAM tori (ie diffeomorphic copies of …

In this paper we consider the case of a general perturbation, for r large enough, of an a priori
unstable Hamiltonian system of 2+ 1/2 degrees of freedom, and we provide explicit …

We study polynomial expansions of local unstable manifolds attached to equilibrium
solutions of parabolic partial differential equations. Due to the smoothing properties of …

We formulate and justify rigorously a numerically efficient criterion for the computation of the
analyticity breakdown of quasi-periodic solutions in symplectic maps (any dimension) and …

This paper presents a methodology for the computation of whole sets of heteroclinic
connections between isoenergetic slices of center manifolds of center center saddle fixed …

The development of efficient methods for detecting quasiperiodic oscillations and computing
the corresponding invariant tori is a subject of great importance in dynamical systems and …