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arXiv · 2604.05174

Entropy and self-intersection number of geodesic currents on compact hyperbolic surfaces

Tina Torkaman
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Abstract

Let $X$ be a compact hyperbolic surface of genus $g$, and $C$ a geodesic current on $X$. Denote by $h_X(C)$ the measure-theoretic entropy of $C$ with respect to the geodesic flow. Assume that $C$ is ergodic. In this paper, we establish a quantitative upper bound on $h_X(C)$ in terms of its self-intersection number $i(C,C)$ and the systole of $X$. In particular, we show that small self-intersection number forces small entropy.

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Tina Torkaman. 2026-04-06. Entropy and self-intersection number of geodesic currents on compact hyperbolic surfaces. https://arxiv.org/abs/2604.05174

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