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arXiv · 2107.14058

The growth and distribution of large circles on translation surfaces

Paul Colognese·Mark Pollicott
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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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Paul Colognese, Mark Pollicott. 2021-07-29. The growth and distribution of large circles on translation surfaces. https://arxiv.org/abs/2107.14058

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