Uniformly Distributed Periodic Orbits of Endomorphisms on n-tori

Abstract

We prove that any ergodic endomorphism on an n-torus admits a sequence of periodic orbits uniformly distributed in the metric sense. As a corollary, an endomorphism on the torus is ergodic if and only if the Haar measure can be approximated by periodic measures.

Keywords

Ergodic / periodic orbit / uniformly distributed / Haar measure / torus / 37D30

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Peking University