Minimal sets of periods for Morse-Smale diffeomorphisms on non-orientable compact surfaces without boundary

Abstract

We study the minimal set of (Lefschetz) periods of the C1 Morse-Smale diffeomorphisms on a non-orientable compact surface without boundary inside its class of homology. In fact our study extends to the C1 diffeomorphisms on these surfaces having finitely many periodic orbits all of them hyperbolic and with the same action on the homology as the Morse-Smale diffeomorphisms. We mainly have two kind of results. First we completely characterize the minimal sets of periods for the C1 Morse-Smale diffeomorphisms on non-orientable compact surface without boundary of genus g with 1 ≤ g ≤ 9. But the proof of these results provides an algorithm for characterizing these minimal sets of periods for the C1 Morse-Smale diffeomorphisms on non-orientable compact surfaces without boundary of arbitrary genus. Second we study what kind of subsets of positive integers can be minimal sets of periods of the C1 Morse-Smale diffeomorphisms on a non-orientable compact surface without boundary.