Stretching the Oxtoby-Ulam Theorem

Volume 84 / 2000

Ethan Akin Colloquium Mathematicum 84 (2000), 83-94 DOI: 10.4064/cm-84/85-1-83-94

Abstract

On a manifold X of dimension at least two, let μ be a nonatomic measure of full support with μ(∂X) = 0. The Oxtoby-Ulam Theorem says that ergodicity of μ is a residual property in the group of homeomorphisms which preserve μ. Daalderop and Fokkink have recently shown that density of periodic points is residual as well. We provide a proof of their result which replaces the dependence upon the Annulus Theorem by a direct construction which assures topologically robust periodic points.

Authors

  • Ethan Akin

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