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 C 1 Morse–Smale diffeomorphisms on a non-orientable compact surface without boundary inside its class of homology. In fact our study extends to the C 1 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 kinds of results. First, we completely characterize the possible minimal sets of periods for the C 1 Morse–Smale diffeomorphisms on non-orientable compact surface without boundary of genus g with . But the proof of these results provides an algorithm for characterizing the possible minimal sets of periods for the C 1 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 C 1 Morse–Smale diffeomorphisms on a non-orientable compact surface without boundary.