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Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches
Advances in Mathematics ( IF 1.7 ) Pub Date : 2021-05-10 , DOI: 10.1016/j.aim.2021.107778
Johannes Jaerisch , Hiroki Takahasi

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.



中文翻译:

具有许多分支的非均匀扩展一维马尔可夫图的Birkhoff平均值的混合多重分形谱

对于具有许多分支和有限许多中性点的区间或圆的马尔可夫图,我们根据不变概率测度的Hausdorff维数,建立了可观数量的Birkhoff平均混合多重分形谱的条件变分公式。使用我们的结果,我们能够展示出新的分形几何结果,用于实数的向后连续分数扩展,尤其是回答了Pollicott的问题。此外,我们建立了与具有抛物线形元素的有限生成的自由Fuchsian群相关的Bowen-Series映射的多尖峰缠绕谱的公式。

更新日期:2021-05-11
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