Uniformly Distributed Periodic Orbits of Endomorphisms on n-tori

Daohua Yu; Shaobo Gan

doi:10.1007/s11464-024-0152-z

Frontiers of Mathematics ›› 2025, Vol. 20 ›› Issue (5) : 961 -978. DOI: 10.1007/s11464-024-0152-z

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Uniformly Distributed Periodic Orbits of Endomorphisms on n-tori

Daohua Yu ¹^,^a
, Shaobo Gan ¹

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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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Daohua Yu, Shaobo Gan. Uniformly Distributed Periodic Orbits of Endomorphisms on n-tori. Frontiers of Mathematics, 2025, 20(5): 961-978 DOI:10.1007/s11464-024-0152-z