Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches

Johannes Jaerisch, Hiroki Takahasi

2 被引用数 (Scopus)

抄録

For a Markov map of an interval or the circle with countably many branches and finitely many neutral points, we establish conditional variational formulas for mixed multifractal spectra of Birkhoff averages of countably many observables, in terms of the Hausdorff dimension of invariant probability measures. Using our results, we are able to exhibit new fractal-geometric results for backward continued fraction expansions of real numbers, answering in particular a question of Pollicott. Moreover, we establish formulas for multi-cusp winding spectra for the Bowen-Series maps associated with finitely generated free Fuchsian groups with parabolic elements.

本文言語 English 107778 Advances in Mathematics 385 https://doi.org/10.1016/j.aim.2021.107778 Published - 2021 7 16

• 数学 (全般)

フィンガープリント

「Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。