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

2015/05/09 by Anton Gorodetski, Gorodetski, Anton, Yakov Pesin +1
Mathematics · #37D25 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1505.02216

openalex publication_date 2015/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Variational principles and approximation of dynamical indicators for\n systems with nonuniformly hyperbolic behavior

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