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

Anton Gorodetski, Yakov Pesin

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

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

Fingerprint

Ergodic Measure
Connectedness
Homoclinic Class
Entropy
Path
Periodic Points
Corollary
Closure
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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

Path connectedness and entropy density of the space of hyperbolic ergodic measures. / Gorodetski, Anton; Pesin, Yakov.

Contemporary Mathematics. American Mathematical Society, 2017. p. 111-121 (Contemporary Mathematics; Vol. 692).

Research output: Chapter in Book/Report/Conference proceedingChapter

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