Unipotent flows on the space of branched covers of Veech surfaces
| dc.creator | Eskin, Alex | |
| dc.creator | Marklof, Jens | |
| dc.creator | Morris, Dave Witte | |
| dc.date | 2004-08-06 | |
| dc.date | 2005-05-09 | |
| dc.date.accessioned | 2026-07-07T05:11:05Z | |
| dc.date.available | 2026-07-07T05:11:05Z | |
| dc.description | There is a natural action of SL(2,R) on the moduli space of translation surfaces, and this yields an action of the unipotent subgroup $U = {\begin{pmatrix} 1 & * 0 & 1 \end{pmatrix}}$. We classify the U-invariant ergodic measures on certain special submanifolds of the moduli space. (Each submanifold is the SL(2,R)-orbit of the set of branched covers of a fixed Veech surface.) For the U-action on these submanifolds, this is an analogue of Ratner's Theorem on unipotent flows. The result yields an asymptotic estimate of the number of periodic trajectories for billiards in a certain family of non-Veech rational triangles, namely, the isosceles triangles in which exactly one angle is $2 π/n$, with $n \ge 5$ and $n$ odd. | |
| dc.description | Added a corollary regarding orbit closures. Greatly expanded the part involving the counting application, giving more detailed proofs and a summary of previous results used | |
| dc.identifier | https://arxiv.org/abs/math/0408090 | |
| dc.identifier | http://arxiv.org/abs/math/0408090 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72125 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Mathematical Physics | |
| dc.subject | 37A99 (primary) 37E15, 37D40, 37D50 (secondary) | |
| dc.title | Unipotent flows on the space of branched covers of Veech surfaces | |
| dc.type | text |