Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure

Roland Gunesch, Anatole B. Katok

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We describe in detail a construction of weakly mixing C diffeomorphisms preserving a smooth measure and a measurable Riemannian metric as well as ℤk actions with similar properties. We construct those as a perturbation of elements of a nontrivial non-transitive circle action. Our construction works on all compact manifolds admitting a nontrivial circle action. It is shown in the appendix that a Riemannian metric preserved by a weakly mixing diffeomorphism can not be square integrable.

Original languageEnglish (US)
Pages (from-to)61-88
Number of pages28
JournalDiscrete and Continuous Dynamical Systems
Volume6
Issue number1
DOIs
StatePublished - 2000

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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