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

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 …

We consider a numerical method based on the so-called “orthogonality condition” for the
approximation and continuation of invariant tori under flows. The basic method was …

This chapter presents some ideas of normally hyperbolic manifold theory, and focuses on
the algorithmic application of the parameterization method in such context. The …

This paper presents an iterative method for locating invariant tori of maps. Specifically,
through the introduction of a shift function on the torus corresponding to the projection of the …

Besonderer Dank gilt meinem Betreuer Werner Vogt für die sorgfältige wissenschaftliche
Betreuung, zahllose inspirierende Gespräche und das teilweise mehrmalige Korrekturlesen …

This thesis is concerned with numerical techniques for resolving and continuing closed,
compact invariant manifolds in parameter-dependent dynamical systems with specific …

Since dynamical systems has a major impact on human development, especially critical
systems that can put human lives at risk if something goes wrong. Hence, the need of …

We show here how, using Euler's integration method and an associated function bounding
the error in function of time, one can generate structures closely surrounding the invariant …