The growth and distribution of large circles on translation surfaces

Colognese, P.; Pollicott, M.

doi:10.1090/ecgd/384

The growth and distribution of large circles on translation surfaces
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by P. Colognese and M. Pollicott;

Conform. Geom. Dyn. 29 (2025), 90-116

DOI: https://doi.org/10.1090/ecgd/384

Published electronically: June 13, 2025

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Abstract:

We consider circles on a translation surface $X$, consisting of points joined to a common center point by a geodesic of length $R$. We show that as $R \to \infty$ these circles distribute to a measure on $X$ which is equivalent to the area. In the last section we consider analogous results for closed geodesics.

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Conformal Geometry and Dynamics

The growth and distribution of large circles on translation surfaces
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Abstract: