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arXiv · 2204.08907

Multifractal analysis of homological growth rates for hyperbolic surfaces

Johannes Jaerisch·Hiroki Takahasi
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Abstract

We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level sets of prescribed growth rates in terms of a generalized Poincar\'e exponent of the Fuchsian group. We employ symbolic dynamics developed by Bowen and Series, ergodic theory and thermodynamic formalism to prove the analyticity of the dimension spectrum.

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Johannes Jaerisch, Hiroki Takahasi. 2022-04-19. Multifractal analysis of homological growth rates for hyperbolic surfaces. https://doi.org/10.1017/etds.2024.62

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