Multifractal analysis of geodesic flows on surfaces without focal points
Multifractal analysis of geodesic flows on surfaces without focal points
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DOI：
10.1080/14689367.2021.1978394
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发表时间：
2021-04
期刊：
影响因子：
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通讯作者：
Kiho Park;Tianyu Wang
中科院分区：
文献类型：
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作者：
Kiho Park;Tianyu Wang
本文研究了无焦点紧致秩1曲面上测地线流的多重分形谱。我们计算的熵的水平集的李雅普诺夫指数，并建立一个下界的Hausdorff维数的压力函数和勒让德变换。在这样做时，我们采用和推广的伯恩斯和Gelfert的非正曲面的结果，并构建一个日益嵌套序列的基本集的补充奇异集上的测地线流是非一致双曲。这样的基本集合序列最终包含任何给定的基本集合。
In this paper, we study multifractal spectra of the geodesic flows on compact rank 1 surfaces without focal points. We compute the entropy of the level sets for the Lyapunov exponents and establish a lower bound for their Hausdorff dimension in terms of the pressure function and its Legendre transform. In doing so, we employ and generalize results of Burns and Gelfert for non-positively curved surfaces and construct an increasingly nested sequence of basic sets in the complement of the singular set on which the geodesic flow is non-uniformly hyperbolic. Such a sequence of basic sets eventually contains any given basic set.