Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Dimension of Markov towers for non uniformly expanding one-dimensional systems

Pages: 1447 - 1464, Volume 9, Issue 6, November 2003      doi:10.3934/dcds.2003.9.1447

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Fernando J. Sánchez-Salas - Departamento de Matemáticas, Facultad Experimental de Ciencias, La Universidad del Zulia, Maracaibo, Venezuela (email)

Abstract: We prove that a non uniformly expanding one-dimensional system defined by an interval map with an ergodic non atomic Borel probability $\mu$ with positive Lyapunov exponent can be reduced to a Markov tower with good fractal geometrical properties. As a consequence we approximate $\mu$ by ergodic measures supported on hyperbolic Cantor sets of arbitrarily large dimension.

Keywords:  Non uniformly expanding systems, absolutely continuous invariant measures, entropy, positive Lyapunov exponents, Markov towers, induced Markov transformations, Hausdorff dimension, Pesin entropy formula.
Mathematics Subject Classification:  37A05, 37C40, 37D25, 37C45.

Received: January 2002;      Revised: March 2003;      Available Online: September 2003.