Divergent on average directions of Teichmüller geodesic flow

DOI10.4171/JEMS/1117zbMath1489.37038arXiv1803.00093MaRDI QIDQ2119382

Paul Apisa, Howard A. Masur

Publication date: 29 March 2022

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.00093

zbMATH Keywords

flat surfacesTeichmüller geodesic flow

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Orbit growth in dynamical systems (37C35) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Teichmüller theory; moduli spaces of holomorphic dynamical systems (37F34)

Cites Work

• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow
• Every flat surface is Birkhoff and Oseledets generic in almost every direction
• Hausdorff dimension of the set of singular pairs
• The Hausdorff dimension of non-uniquely ergodic directions in \(H(2)\) is almost everywhere \(1/2\)
• Lines of minima and Teichmüller geodesics
• Ergodicity of billiard flows and quadratic differentials
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• Hausdorff dimension of the set of nonergodic foliations of a quadratic differential
• Harmonic maps, length, and energy in Teichmüller space
• Diophantine approximations for translation surfaces and planar resonant sets
• Singular systems of linear forms and non-escape of mass in the space of lattices
• Exceptional directions for the Teichmüller geodesic flow and Hausdorff dimension
• The set of non-uniquely ergodic \(d\)-IETs has Hausdorff codimension 1/2
• Thick-thin decomposition for quadratic differentials
• Hausdorff Dimension of Divergent Teichmuller Geodesics
• The growth rate of trajectories of a quadratic differential
• On Khintchine exponents and Lyapunov exponents of continued fractions
• Divergent trajectories of flows on homogeneous spaces and Diophantine approximation.
• Comparison of hyperbolic and extremal lengths
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