Dynamics of annulus maps II: periodic points for coverings

Jorge Iglesias, Aldo Portela, Alvaro Rovella, Juliana Xavier

Published 2014-11-20Version 1

Let $f$ be a covering map of the open annulus $A= S^1\times (0,1)$ of degree $d$ , $|d|>1$. Assume that $f$ preserves an essential (i.e not contained in a disk of $A$) compact subset $K$. We show that $f$ has at least the same number of periodic points in each period as the map $z^d$ in $S^1.$