On the set of periods for the Morse-Smale diffeomorphisms on the disc with N holes

Let Dn be the two-dimensional disc with n holes. We assume that Dn is compact. For every homological class of Morse-Smale diffeomorphisms on Dn without periodic points in its boundary, we provide an algorithm for characterizing its minimal set of Lefschetz periods. We give the complete classification of these sets of periods for. The main tool used for this characterization is the Lefschetz zeta function. © 2013 Copyright Taylor and Francis Group, LLC.