### 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 |

### 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