Hyperbolic periodic points for chain hyperbolic homoclinic classes

2015/05/22 by Sun, Wenxiang, Yang, Yun
#37C29 #37D20 #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.06148

Abstract

In this paper we establish a closing property and a hyperbolic closing property for thin trapped chain hyperbolic homoclinic classes with one dimensional center in partial hyperbolicity setting. Taking advantage of theses properties, we prove that the growth rate of the number of hyperbolic periodic points is equal to the topological entropy. We also obtain that the hyperbolic periodic measures are dense in the space of invariant measures.

Related

• Continuum-wise hyperbolicity and periodic points
• Path connectedness and entropy density of the space of ergodic hyperbolic measures
• The structure of the space of ergodic measures of transitive partially\n hyperbolic sets
• Statistical stability for diffeomorphisms with mostly expanding and mostly contracting centers
• Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes