09/09/2016, 16:20 — 17:00 — Amphitheatre Pa2, Mathematics Building
Carlos Rocha, Instituto Superior Técnico, Universidade de Lisboa

On a definition of Morse-Smale evolution processes

We consider a definition of Morse-Smale evolution process that extends the notion of Morse-Smale dynamical system to the nonautonomous framework. In particular we consider nonautonomous perturbations of autonomous systems. In this case our definition of Morse-Smale evolution process holds for perturbations of Morse-Smale autonomous systems with or without periodic orbits. We establish that small nonautonomous perturbations of autonomous Morse-Smale evolution processes derived from certain nonautonomous differential equations are Morse-Smale evolution processes. We apply our results to examples of scalar parabolic semilinear differential equations generating evolution processes and possessing periodic orbits.

This is a joint work with Radoslaw Czaja and Waldyr Oliva.