On dirac physical measures for transitive flows

Radu Saghin, Wenxiang Sun, Edson Vargas

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We discuss some examples of smooth transitive flows with physical measures supported at fixed points. We give some conditions under which stopping a flow at a point will create a Dirac physical measure at that indifferent fixed point. Using the Anosov-Katok method, we construct transitive flows on surfaces with the only ergodic invariant probabilities being Dirac measures at hyperbolic fixed points. When there is only one such point, the corresponding Dirac measure is necessarily the only physical measure with full basin of attraction. Using an example due to Hu and Young, we also construct a transitive flow on a three-dimensional compact manifold without boundary, with the only physical measure the average of two Dirac measures at two hyperbolic fixed points.

Original languageEnglish
Pages (from-to)741-756
Number of pages16
JournalCommunications in Mathematical Physics
Volume298
Issue number3
DOIs
StatePublished - 2010
Externally publishedYes

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