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Autor: Athreya, J. S., Fairchild, S., Masur, H.

Publikováno v: Advances in Mathematics, Volume 431, 2023, 109233, ISSN 0001-8708

We show that for almost every translation surface the number of pairs of saddle connections with bounded magnitude of the cross product has asymptotic growth like $c R^2$ where the constant $c$ depends only on the area and the connected component of

Externí odkaz: http://arxiv.org/abs/2201.08628

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Akademický článek

Counting pairs of saddle connections

Autor: Athreya, J.S., Fairchild, S., Masur, H.

Publikováno v: In Advances in Mathematics 15 October 2023 431

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Minimal nonergodic directions on genus 2 translation surfaces

Autor: Cheung, Y., Masur, H.

Publikováno v: Ergodic Th. Dynam. Sys. 26 (2006), 341--351.

It is well-known that on any Veech surface, the dynamics in any minimal direction is uniquely ergodic. In this paper it is shown that for any genus 2 translation surface which is not a Veech surface there are uncountably many minimal but not uniquely

Externí odkaz: http://arxiv.org/abs/math/0501286

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A divergent Teichmuller geodesic with uniquely ergodic vertical foliation

Autor: Cheung, Y., Masur, H.

Publikováno v: Israel J. Math. 152 (2006), 1--15.

We construct an example of a quadratic differential whose vertical foliation is uniquely ergodic and such that the Teichmuller geodesic determined by the quadratic differential diverges in the moduli space of Riemann surfaces.
Comment: 16 pages,

Externí odkaz: http://arxiv.org/abs/math/0501296

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