Dynamics of annulus coverings II: periodic points

Abstract

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 $S^1.$

Improved version after referee. To appear in Fundamenta Math

References in corpus (1)

• Dynamics of covering maps of the annulus I: semiconjugacies

Cited by in corpus (2)

• Dynamics of annulus maps III: completeness
• Fixed points for branched covering maps of the plane