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November  2003, 9(6): 1447-1464. doi: 10.3934/dcds.2003.9.1447

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

1. 

Departamento de Matemáticas, Facultad Experimental de Ciencias, La Universidad del Zulia, Maracaibo, Venezuela

Received  January 2002 Revised  March 2003 Published  September 2003

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.
Citation: Fernando J. Sánchez-Salas. Dimension of Markov towers for non uniformly expanding one-dimensional systems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1447-1464. doi: 10.3934/dcds.2003.9.1447
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