New phenomena in deviation of Birkhoff integrals for locally Hamiltonian flows

DOI10.1515/crelle-2023-0090arXiv2112.13030OpenAlexW4390483693MaRDI QIDQ6191982

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Publication date: 12 February 2024

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.13030

zbMATH Keywords

ergodicityHamiltonian flowsTeichmüller flowcompact surfacesBirkhoff integralsrenormalization cocycle

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Cites Work

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• Hölder regularity of the solutions of the cohomological equation for Roth type interval exchange maps
• Cocycles over interval exchange transformations and multivalued Hamiltonian flows
• Absence of mixing in area-preserving flows on surfaces
• Ergodic properties of infinite extensions of area-preserving flows
• Gauss measures for transformations on the space of interval exchange maps
• Solutions of the cohomological equation for area-preserving flows on compact surfaces of higher genus
• Deviation of ergodic averages for area-preserving flows on surfaces of higher genus
• Quantitative mixing for locally Hamiltonian flows with saddle loops on compact surfaces
• Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents
• Absence of mixing for smooth flows on genus two surfaces
• Weak mixing for logarithmic flows over interval exchange transformations
• Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture
• Limit theorems for translation flows
• Singularity of the spectrum for smooth area-preserving flows in genus two and translation surfaces well approximated by cylinders
• Échanges d'intervalles et transformations induites
• Deviation for interval exchange transformations
• A smooth mixing flow on a surface with nondegenerate fixed points
• Sobolev regularity of solutions of the cohomological equation
• Lebesgue spectrum of countable multiplicity for conservative flows on the torus
• Mixing of asymmetric logarithmic suspension flows over interval exchange transformations
• The cohomological equation for Roth-type interval exchange maps
• Interval exchange transformations

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