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 …

We present a KAM theory for some dissipative systems (geometrically, these are conformally
symplectic systems, ie systems that transform a symplectic form into a multiple of itself). For …

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 …

We present several algorithms for computing normally hyperbolic invariant tori carrying
quasi-periodic motion of a fixed frequency in families of dynamical systems. The algorithms …

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 …

This lecture describes validated numerical tools which are used for global analysis of
nonlinear systems. The main focus is dynamics near and between equilibrium solutions of …

The goal of this paper is to present a methodology for the computation of invariant tori in
Hamiltonian systems combining flow map methods, parameterization methods, and …

We consider the dissipative spin–orbit problem in Celestial Mechanics, which describes the
rotational motion of a triaxial satellite moving on a Keplerian orbit subject to tidal forcing and …

We present results towards a constructive approach to show the existence of quasi-periodic
solutions in non-perturbative regimes of some dissipative systems, called conformally …

We consider the problem of numerically computing quasi-periodic normally hyperbolic
invariant tori (NHIT) with fixed frequency as well as their invariant bundles. The algorithm is …