Periodic points of equivariant maps - Jezierski, Jerzy; Marzantowicz, Waclaw (MATHEMATICA SCANDINAVICA, 2010)
We assume that X is a compact connected polyhedron, G is a finite group acting freely on X, and f:X→ X a G-equivariant map. We find formulae for the least number of n-periodic points in the equivariant homotopy class of f, i.e., _h |(Fix(h^n)| (where h is G-homotopic to f). As an application we prove that the set of periodic points of an equivariant map is infinite provided the action on the rational homology of X is trivial and the Lefschetz number L(f^n) does not vanish for infinitely many indices n commeasurable with the order of G. Moreover, at least linear growth, in n, of the number of points of period n is shown.