Recent advances in global dynamics

Rafael Luís

One of the main objectives in the area of discrete dynamical systems or difference equations is the study of the qualitative properties of fixed points. Particularly, in population dynamics, we are interested in global stability of fixed points or periodic orbits.

In this talk we will present the principal notions of stability and give a short resume of the recent developments in global stability. We will illustrate our results with some important models in population dynamics.