Effective counting on translation surfaces
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Publication:2281325
DOI10.1016/j.aim.2019.106890zbMath1451.37049arXiv1708.06263OpenAlexW2986332204WikidataQ126811979 ScholiaQ126811979MaRDI QIDQ2281325
Barak Weiss, Amos Nevo, Rene Rühr
Publication date: 19 December 2019
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1708.06263
Ergodic theory on groups (22D40) Ergodic theorems, spectral theory, Markov operators (37A30) Orbit growth in dynamical systems (37C35) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)
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Counting pairs of saddle connections ⋮ Uniform distribution of saddle connection lengths in all \(\mathrm{SL}(2,\mathbb{R})\) orbits ⋮ Siegel-Veech transforms are in \(L^2\) ⋮ Uniform distribution of saddle connection lengths (with an appendix by Daniel El-Baz and Bingrong Huang) ⋮ Counting saddle connections in a homology class modulo \( q \) (with an appendix by Rodolfo Gutiérrez-Romo) ⋮ ENUMERATION OF MEANDERS AND MASUR–VEECH VOLUMES ⋮ Effective counting for discrete lattice orbits in the plane via Eisenstein series ⋮ On convergence of random walks on moduli space
Cites Work
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- Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow
- Isolation, equidistribution, and orbit closures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
- Exponential mixing for the Teichmüller flow
- Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture
- Non-Abelian harmonic analysis. Applications of \(SL(2,{\mathbb{R}})\)
- Siegel measures
- Moduli spaces of Abelian differentials: the principal boundary, counting problems, and the Siegel-Veech constants
- Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
- Siegel-Veech transforms are in \(L^2\)
- Asymptotic formulas on flat surfaces
- The growth rate of trajectories of a quadratic differential
- The rate of mixing for geodesic and horocycle flows
