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arXiv · 0803.1522

Birkhoff spectra for one-dimensional maps with some hyperbolicity

Yong Moo Chung
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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 $C^2$ 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.

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Yong Moo Chung. 2008-03-11. Birkhoff spectra for one-dimensional maps with some hyperbolicity. https://arxiv.org/abs/0803.1522

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