Multifractal analysis of Birkhoff averages for countable Markov maps

Details Multifractal analysis of Birkhoff averages for countable Markov maps Multifractal analysis of Birkhoff averages for countable Markov maps

2010-03-15

arxiv.org/abs/1003.2979v4

Mathematics

Dynamical Systems

27 pages. Substantial changes have been made to Theorem 1.2 and sections 4,5 and 6. Some minor corrections have been made else

Scientific paper

In this paper we prove a multifractal formalism of Birkhoff averages for interval maps with countably many branches. Furthermore, we prove that under certain regularity assumptions on the potential the Birkhoff spectrum is real analytic. Applications of these results to number theory are also given. Finally, we compute the Hausdorff dimension of the set of points for which the Birkhoff average is infinite.

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