On Hölder-continuity of Oseledets subspaces

DOI10.1112/jlms/jdv057zbMath1362.37010arXiv1409.8167OpenAlexW3099379970MaRDI QIDQ2793766

Vítor Araújo, Simion Filip, Alexander I. Bufetov

Publication date: 17 March 2016

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

Full work available at URL: https://arxiv.org/abs/1409.8167

zbMATH Keywords

Teichmüller flowKontsevich-Zorich cocycleTeichmüller diskHölder cocyclesvector bundle automorphism

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Dynamical systems involving one-parameter continuous families of measure-preserving transformations (37A10)

Related Items (5)

Continuity of Lyapunov exponents is equivalent to continuity of Oseledets subspaces ⋮ Measure rigidity of Anosov flows via the factorization method ⋮ Hölder continuity of Oseledets splittings for semi-invertible operator cocycles ⋮ Non-stationary smooth geometric structures for contracting measurable cocycles ⋮ Kummer rigidity for K3 surface automorphisms via Ricci-flat metrics

Cites Work

• Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow
• Every flat surface is Birkhoff and Oseledets generic in almost every direction
• Isolation, equidistribution, and orbit closures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
• Exponential mixing for the Teichmüller flow
• Deviation of ergodic averages for area-preserving flows on surfaces of higher genus
• Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
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