BIRKHOFF SPECTRA FOR ONE-DIMENSIONAL MAPS WITH SOME HYPERBOLICITY

2010/02/04 by YONG MOO CHUNG, Yong Moo Chung · 2 citations
Mathematics · #Mathematical Dynamics and Fractals

paper · doi:10.1142/s021949371000284x

Abstract

We study the multifractal analysis for smooth dynamical systems in dimension one. It is given a characterization of the Hausdorff dimension of the level set obtained from the Birkhoff averages of a continuous function by the local dimensions of hyperbolic measures for a topologically mixing C 2 map modeled by an abstract dynamical system. A characterization which corresponds to above is also given for the ergodic basins of invariant probability measures. And it is shown that the complement of the set of quasi-regular points carries full Hausdorff dimension.

Citations

• Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
• Statistical Properties of Dynamical Systems with Some Hyperbolicity
• Some relations between dimension and Lyapounov exponents

Cited by

• Multifractal analysis of weighted ergodic averages
• Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems

Related

• Birkhoff spectra for one-dimensional maps with some hyperbolicity
• Multifractal analysis of non-uniformly hyperbolic systems
• Multifractal analysis of dimension spectrum and the set of irregular points in non-uniformly hyperbolic systems
• Multifractal analysis of the divergence points of Birkhoff averages in beta-dynamical systems
• Multifractal analysis of weak Gibbs measures for non-uniformly expanding C¹ maps