Horospherical dynamics in invariant subvarieties

Foliations in differential topology; geometric theory (57R30) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Foliations generated by dynamical systems (37C86)

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
Invariant Radon measures on measured lamination space
The Teichmüller geodesic flow
Invariant measures and minimal sets of horospherical flows
Invariant measures of horospherical flows on non-compact homogeneous spaces
Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
Minimal sets for flows on moduli space
Effective counting of simple closed geodesics on hyperbolic surfaces
Cylinder deformations in orbit closures of translation surfaces
Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards
Translation surfaces and their orbit closures: an introduction for a broad audience
Dynamics of \(\text{SL}_2(\mathbb R)\) over moduli space in genus two
Asymptotic formulas on flat surfaces
Introduction to Smooth Manifolds
Ergodic Theory of the Space of Measured Laminations
Subadditive mean ergodic theorems
Nondivergence of horocyclic flows on moduli space
Veech surfaces and complete periodicity in genus two
Limits of geodesic push-forwards of horocycle invariant measures
Horocycle Dynamics: New Invariants and Eigenform Loci in the Stratum ℋ(1,1)
Cohomology classes represented by measured foliations, and Mahler's question for interval exchanges
Ergodic Theory
Geometric Structures on Manifolds

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