This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-
time dynamical systems with concrete instruction on implementations (and example …

Incorporating quasi-periodic orbits into the preliminary design process offers a wide range of
options to meet mission constraints and address the challenges in a complex trade space. In …

A tutorial on continuation and bifurcation methods for the analysis of truncated dissipative
partial differential equations is presented. It focuses on the computation of equilibria …

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 …

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

Quasi-periodic invariant tori are of great interest in astrodynamics because of their capability
to further expand the design space of satellite missions. However, there is no general …

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 …

The Martian Moons eXploration mission, currently under development by the Japan
Aerospace Exploration Agency (JAXA), will be launched in 2024 with the goal of retrieving …

In two previous papers [J. Differential Equations, 228 (2006), pp. 530-579; Discrete Contin.
Dyn. Syst. Ser. B, 6 (2006), pp. 1261-1300] we have developed fast algorithms for the …