Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches
Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches
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DOI：
10.1016/j.aim.2021.107778
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发表时间：
2020-04
影响因子：
1.7
通讯作者：
Johannes Jaerisch;Hiroki Takahasi
中科院分区：
文献类型：
--
作者：
Johannes Jaerisch;Hiroki Takahasi
对于具有可数个分支和有限个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豪斯多夫维数，建立了可数个可观测量的 Birkhoff 平均值的混合多重分形谱的条件变分公式。利用我们的结果，我们能够展示实数向后连分数展开的新分形几何结果，特别回答了波利科特的问题。此外，我们为与有限生成的具有抛物线元素的自由 Fuchsian 群相关的 Bowen 级数映射建立了多尖点缠绕谱的公式。
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.