Gaps of saddle connection directions for some branched covers of tori

DOI10.1017/etds.2021.81zbMath1505.37008arXiv2004.04182OpenAlexW3189200128WikidataQ114118693 ScholiaQ114118693MaRDI QIDQ5868368

Anthony Sanchez

Publication date: 20 September 2022

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.04182

zbMATH Keywords

gap distributionPoincaré sectionhorocycle flowtranslation surfaceaffine lattice

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Homogeneous flows (37A17)

Related Items (1)

Slope gap distribution of saddle connections on the \(2n\)-gon

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Poincaré sections for the horocycle flow in covers of \(\mathrm {SL}(2,\mathbb {R})/\mathrm {SL}(2,\mathbb {Z})\) and applications to Farey fraction statistics
• The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems
• Dichotomy for the Hausdorff dimension of the set of nonergodic directions
• Invariant measures and minimal sets of horospherical flows
• On measure rigidity of unipotent subgroups of semisimple groups
• On Raghunathan's measure conjecture
• Hausdorff dimension of the set of nonergodic directions (with an Appendix by M. Boshernitzan)
• Strict measure rigidity for unipotent subgroups of solvable groups
• Closed trajectories for quadratic differentials with an application to billiards
• On the asymptotic quadratic growth rate of saddle connections and periodic orbits on marked flat tori.
• Gaps in \(\sqrt{n}\bmod 1\) and ergodic theory
• The distribution of gaps for saddle connection directions
• Equidistribution of saddle connections on translation surfaces
• A transversal for horocycle flow on \(\mathcal{H}(\alpha)\)
• An effective Ratner equidistribution result for SL\((2,\mathbb R)\ltimes \mathbb R^2\)
• Dynamics of \(\text{SL}_2(\mathbb R)\) over moduli space in genus two
• Asymptotic formulas on flat surfaces
• The gap distribution of slopes on the golden L
• A Poincaré Section for the Horocycle Flow on the Space of Lattices
• Gap distributions and homogeneous dynamics
• Unipotent flows on the space of branched covers of Veech surfaces
• The Distribution of Gaps for Saddle Connections on the Octagon

This page was built for publication: Gaps of saddle connection directions for some branched covers of tori