Birkhoff spectra for one-dimensional maps with some hyperbolicity
Dynamical Systems
2008-03-12 v1
Abstract
We study the multifractal analysis for smooth dynamical systems in dimension one. It is characterized 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 map modelled 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.
Cite
@article{arxiv.0803.1522,
title = {Birkhoff spectra for one-dimensional maps with some hyperbolicity},
author = {Yong Moo Chung},
journal= {arXiv preprint arXiv:0803.1522},
year = {2008}
}
Comments
21 pages