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...

We present a Kolmogorov-like algorithm for the computation of normal form in neighborhood an invariant torus `isochronous' Hamiltonian systems, i.e., systems with Hamiltonians $\mathcal{H}=\mathcal{H}_0+\varepsilon \mathcal{H}_1$ where $\mathcal{H}_0$ is $N$ linear oscillators, and $\mathcal{H}_1$ expandable as polynomial series oscillators' canonical variables. This method can be regarded anal...

We present a method for constructing a partition of an incomplete horseshoe in a Poincare map. The partition is based only on the unstable manifolds of the outermost fixed points and eventually their limits. Consequently, this partition becomes natural from the point of view of asymptotic scattering observations. The symbolic dynamics derived from this partition coincides with the one derived f...

The purpose of this paper is the semi-analytical computation of the bounded orbits of Hill's equations, describing the relative motion of two particles in their Keplerian motion around a central body. We have considered the case in which one of the particles moves along a circular reference orbit. The solutions obtained are the generalisation of the usual periodic orbits obtained for the linear...