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

Anton Gorodetski; Yakov Pesin

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

Dynamical Systems 2017-06-09 v2

Authors: Anton Gorodetski , Yakov Pesin

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 homoclinically related. As a corollary we obtain that the closure of this space is also path connected.

Keywords

hyperbolic ergodic measure path connectedness entropy density isolated homoclinic class homoclinic relation hyperbolic periodic point measure space dynamical systems

Cite

@article{arxiv.1505.02216,
  title  = {Path connectedness and entropy density of the space of ergodic hyperbolic measures},
  author = {Anton Gorodetski and Yakov Pesin},
  journal= {arXiv preprint arXiv:1505.02216},
  year   = {2017}
}

Comments

9 pages

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