Multifractal analysis for historic set in topological dynamical systems

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)).

30 pages

References in corpus (2)

• Lyapunov spectrum of asymptotically sub-additive potentials
• Topological pressure of simultaneous level sets

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