We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt–Poincaré technique. As illustrative examples we choose one–dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.

We summarize some numerical works on the analyticity properties of the perturbative series (e. g. Lindstedt series) for some simple discrete-time hamiltonian systems like the so-called \standard map" and generalizations. We stress the relevance of our results for the development of a renormalization group picture based on perturbation theory.

Inspired by the quantum eld theory, a resummation is performed in the Lindstedt series deening the KAM tori, and a possible mechanism for universality of the tori breakdown is discussed. This work is mostly based on a joint paper with G. Gallavotti.

This paper examines the recurrent behaviour of a class of hybrid systems which periodically switch between diierent rst order integrators. The analysis is based on studying the Poincare map of the hybrid system. For switched integrator systems, the Poincare maps are linear mappings thereby allowing easy characterization of the system's stability. Extending these results to more general classes ...

We present Poincare invariant domain wall (“3-brane”) solutions to some 5-dimensional effective theories which can arise naturally in string theory. In particular, we find theories where Poincare invariant solutions exist for arbitrary values of the brane tension, for certain restricted forms of the bulk interactions. We describe examples in string theory where it would be natural for the quant...