### 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 language | English (US) |
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Title of host publication | Contemporary Mathematics |

Publisher | American Mathematical Society |

Pages | 111-121 |

Number of pages | 11 |

DOIs | |

State | Published - Jan 1 2017 |

### Publication series

Name | Contemporary Mathematics |
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Volume | 692 |

ISSN (Print) | 0271-4132 |

ISSN (Electronic) | 1098-3627 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Contemporary Mathematics*(pp. 111-121). (Contemporary Mathematics; Vol. 692). American Mathematical Society. https://doi.org/10.1090/conm/692/13905

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Path connectedness and entropy density of the space of hyperbolic ergodic measures

AU - Gorodetski, Anton

AU - Pesin, Yakov

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=85029156922&partnerID=8YFLogxK

U2 - 10.1090/conm/692/13905

DO - 10.1090/conm/692/13905

M3 - Chapter

AN - SCOPUS:85029156922

T3 - Contemporary Mathematics

SP - 111

EP - 121

BT - Contemporary Mathematics

PB - American Mathematical Society

ER -