Title: From order to chaos: the role of the invariant manifolds

Author: Carles Sim\'o
        Departament de Matem\`atica Aplicada i An\`alisi
        Universitat de Barcelona, Barcelona, Catalunya
        {\tt carles@maia.ub.es}

Talk delivered at the 16$^{\mbox{a}}$ Trobada Matem\`atica, 
Societat Catalana de Matem\`atiques, Barcelona, June 17, 2013

Abstract:

In Dynamical Systems there are some key objects which are part of the skeleton
of the system: the invariant objects. When they are hyperbolic (perhaps in a
partial or weak sense) the related invariant manifolds guide the dynamics.
The relative positions of these manifolds and the changes with respect to
parameters allow to understand the transitions from order to chaos.