Minimal sets for flows on moduli space

DOI10.1007/BF02771535zbMath1052.37025MaRDI QIDQ1881743

John Smillie, Barak Weiss

Publication date: 15 October 2004

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Teichmüller disksquadratic differentialsinterval exchange transformationhorocycle flowminimal setsstratarational polygonal billiards

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

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Cites Work

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• Moduli spaces of quadratic differentials
• Hausdorff dimension of sets of nonergodic measured foliations
• Quadratic differentials with prescribed singularities and pseudo-Anosov diffeomorphisms
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Connected components of the strata of the moduli spaces of quadratic differentials
• Measures supported on the set of uniquely ergodic directions of an arbitrary holomorphic 1-form
• Nondivergence of horocyclic flows on moduli space
• Veech surfaces and complete periodicity in genus two