Hyperbolic periodic points for chain hyperbolic homoclinic classes
Copyright policy )Hyperbolic periodic points for chain hyperbolic homoclinic classes
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.
15 pages, 1 figures
Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.), Topological entropy, closing property, maximal entropy measures, Dynamical Systems (math.DS), chain hyperbolicity, 37D30, 37D20, 37C29, Dynamical systems with hyperbolic orbits and sets, growth of periodic points, topological entropy, FOS: Mathematics, Homoclinic and heteroclinic orbits for dynamical systems, Mathematics - Dynamical Systems, Partially hyperbolic systems and dominated splittings
Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.), Topological entropy, closing property, maximal entropy measures, Dynamical Systems (math.DS), chain hyperbolicity, 37D30, 37D20, 37C29, Dynamical systems with hyperbolic orbits and sets, growth of periodic points, topological entropy, FOS: Mathematics, Homoclinic and heteroclinic orbits for dynamical systems, Mathematics - Dynamical Systems, Partially hyperbolic systems and dominated splittings
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