Multifractal analysis for historic set in topological dynamical systems
Dynamical Systems
2015-06-12 v1
Abstract
In this article, the historic set is divided into different level sets and we use topological pressure to describe the size of these level sets. We give an application of these results to dimension theory. Especially, we use topological pressure to describe the relative multifractal spectrum of ergodic averages and give a positive answer to the conjecture posed by L. Olsen (J. Math. Pures Appl. {\bf 82} (2003)).
Cite
@article{arxiv.1212.4337,
title = {Multifractal analysis for historic set in topological dynamical systems},
author = {Xiaoyao Zhou and Ercai Chen},
journal= {arXiv preprint arXiv:1212.4337},
year = {2015}
}
Comments
30 pages