论文标题
Birkhoff平均的混合多纹状光谱，用于非均匀扩展的一维Markov地图，具有许多分支
Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches
论文作者
论文摘要
对于一个间隔的马尔可夫图或具有数量有限的中性周期点有限的圆形的马尔可夫地图，我们就不可分割的概率概率度量的Hausdorff维度来建立了Birkhoff平均混合多型谱的条件变异公式。利用我们的结果，我们能够展示新的分形结果，以延续实际数字的持续分数，特别是回答了Pollicott的问题。此外，我们为与有限生成的带有抛物线元素的自由紫色群体相关的Bowen系列地图建立了多CUSP绕组光谱的公式。
For a Markov map of an interval or the circle with countably many branches and finitely many neutral periodic points, we establish conditional variational formulas for the 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.
