Periods of self-maps on via their homology

Abstract

UDC 517.9 As usual, we denote а 2 -dimensional sphere  by . We study the periods of  periodic orbits of the maps that are either continuous or C 1 with all their periodic orbits being hyperbolic, or transverse, or holomorphic, or transverse holomorphic. For the first time, we summarize all  known results on the periodic orbits of these distinct kinds of self-maps on together. We note that every time when a map increases its structure, the number of  periodic orbits provided by its action on the homology increases.