Minimal number of periodic points for smooth self-maps of two-holed 3-dimensional closed ball

Abstract

Let $M$ be two-holed $3$-dimensional closed ball, $r$ a given natural number. We consider $f$, a continuous self-map of $M$ with real eigenvalues on the second homology group, and determine the minimal number of $r$-periodic points for all smooth maps homotopic to $f$.