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 …

This paper is devoted to the analysis of an extended neighborhood of the collinear
equilibrium points of the restricted three body problem. The analysis is done using numerical …

Quasi-halo orbits in the circular restricted three-body problem are quasi-periodic orbits that
exist about the periodic halo orbits. A quasi-periodic orbit is an orbit diffeomorphic to a quasi …

Many systems in science and engineering can be modeled as coupled or forced nonlinear
oscillators, which may possess quasi-periodic or phase-locked invariant tori. Since there …

In this paper we prove rigorous results on persistence of invariant tori and their whiskers.
The proofs are based on the parameterization method of [X. Cabré, E. Fontich, R. de la …

This paper first summarizes the theory of quasi-periodic bifurcations for dissipative
dynamical systems. Then it presents algorithms for the computation and continuation of …

Examining the properties of quasi-periodic orbits provides insight into the Sun-perturbed
environment in cislunar space. In this investigation, quasi-periodic trajectories and their …

We describe a numerical method for computing the linearized normal behaviour of an
invariant curve of a diffeomorphism of Bbb R n, n⩾ 2. In the reducible case, the method …

We develop numerical algorithms for the computation of invariant manifolds in quasi-
periodically forced systems. We show how to compute invariant tori and invariant manifolds …

A low-dimensional model of general circulation of the atmosphere is investigated. The
differential equations are subject to periodic forcing, where the period is one year. A three …