Abstract

Despite being widely studied and understood, nonlinear differential systems still lack a formal framework for one important sections, such as Poincare maps. In applications, expressions of these maps strongly depend on the spectrum of the matrix. So it is usual to split their study into cases.
In this talk we provide expressions for Poincare maps of linear differential systems in $Rn$ which are "independent" of both the spectrum of the matrix and the cross section. As an application we discuss the behaviour of the Poincaré map in a neighbourhood of a contact point when n=3. This issue is related to both the existence of reversible periodic orbits and the period doubling phenomena appearing in the Michelson system, it also relates to the study of the flow in the neighbourhood of Teixeira singularities of discontinuous field.

The talk will be in spanish although the slides will be in english.