Homotopy minimal periods for expanding maps on infra-nilmanifolds

Abstract

We prove that the sets of homotopy minimal periods for expanding maps on n-dimensional infra-nilmanifolds are uniformly cofinite, i.e., there exists a positive integer m₀, which depends only on n, such that for any integer m≥m₀, for any n-dimensional infra-nilmanifold M, and for any expanding map f on M, any self-map on M homotopic to f has a periodic point of least period m, namely, [m₀,∞)⊂HPer(f). This extends the main result, Theorem 4.6, of [13] from periods to homotopy periods.