Homotopy minimal periods for expanding maps on infra-nilmanifolds

摘要

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 m_0, which depends only on n, such that for any integer m ≥ m_0, 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, [m_0, ∞) is contained in HPer(f). This extends the main result, Theorem 4.6, of [13] from periods to homotopy periods.