Path connectedness and entropy density of the space of hyperbolic ergodic measures

Anton Gorodetski, Yakov Pesin

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Scopus citations

Abstract

We show that the space of hyperbolic ergodic measures of a given index supported on an isolated homoclinic class is path connected and entropy dense provided that any two hyperbolic periodic points in this class are ho-moclinically related. As a corollary we obtain that the closure of this space is also path connected.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages111-121
Number of pages11
DOIs
StatePublished - Jan 1 2017

Publication series

NameContemporary Mathematics
Volume692
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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  • Cite this

    Gorodetski, A., & Pesin, Y. (2017). Path connectedness and entropy density of the space of hyperbolic ergodic measures. In Contemporary Mathematics (pp. 111-121). (Contemporary Mathematics; Vol. 692). American Mathematical Society. https://doi.org/10.1090/conm/692/13905