Entropy and self-intersection number of geodesic currents on compact hyperbolic surfaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908941359775744 |
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| author | Torkaman, Tina |
| author_facet | Torkaman, Tina |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_05174 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entropy and self-intersection number of geodesic currents on compact hyperbolic surfaces Torkaman, Tina Dynamical Systems Differential Geometry Geometric Topology 37D40, 37E35, 37B10, 53C22 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. |
| title | Entropy and self-intersection number of geodesic currents on compact hyperbolic surfaces |
| topic | Dynamical Systems Differential Geometry Geometric Topology 37D40, 37E35, 37B10, 53C22 |
| url | https://arxiv.org/abs/2604.05174 |