Abstract:

We study the minimal set of periods for Morse-Smale diffeomorphisms on compact surfaces without boundary. In order to do that we introduce the concept of minimal set of Lefschetz periods. We characterize the possible minimal sets of periods on surfaces of low genus and give an algorithm for finding the possible minimal set of periods on surfaces on any genus. We also study what kind of subsets of positive integers can be minimal sets of periods for Morse-Smale diffeomorphisms on a compact surface without boundary. We also show the differences in the minimal set of periods between Morse-Smale diffeomorphisms on orientable surfaces and non-orientable surfaces.

In collaboration with J. Llibre.