A note on homotopy minimal periods for hyperbolic maps on   infra-nilmanifolds
  In this paper, we show that for every non-nilpotent hyperbolic map $f$ on an infra-nilmanifold, the $\textrm{HPer}(f)$ is cofinite in $\mathbb{N}$. This generalizes a similar result for expanding maps. Moreover, we prove that for every nilpotent map $f$ on an infra-nilmanifold, $\textrm{HPer}(f)=\{1\}$. 
Karel Dekimpe, Gert-Jan Dugardein
math.DS math.AT math.GT