# Periodic points of equivariant maps

## DOI:

https://doi.org/10.7146/math.scand.a-15153## Abstract

We assume that $X$ is a compact connected polyhedron, $G$ is a finite group acting freely on $X$, and $f:X\to X$ a $G$-equivariant map. We find formulae for the least number of $n$-periodic points in the equivariant homotopy class of $f$, i.e., $\inf_h |(\mathrm{Fix}(h^n)|$ (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.## Downloads

## Published

2010-12-01

## How to Cite

*MATHEMATICA SCANDINAVICA*,

*107*(2), 224–248. https://doi.org/10.7146/math.scand.a-15153

## Issue

## Section

Articles