Ergodic properties of infinite extensions of area-preserving flows

DOI10.1007/s00208-011-0764-yzbMath1280.37004arXiv1102.5358OpenAlexW1975646197MaRDI QIDQ695276

Corinna Ulcigrai, Krzysztof Frączek

Publication date: 20 December 2012

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.5358

zbMATH Keywords

Hamiltonianergodicitydifferential equationMorse functionarea-preserving flow

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Dynamical systems involving one-parameter continuous families of measure-preserving transformations (37A10) Nonsingular (and infinite-measure preserving) transformations (37A40)

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Singularity of the spectrum for smooth area-preserving flows in genus two and translation surfaces well approximated by cylinders ⋮ Quantitative mixing for locally Hamiltonian flows with saddle loops on compact surfaces ⋮ Dependency of the positive and negative long-time behaviors of flows on surfaces ⋮ New phenomena in deviation of Birkhoff integrals for locally Hamiltonian flows ⋮ Ratner’s property and mild mixing for smooth flows on surfaces ⋮ Non-ergodic \(\mathbb{Z}\)-periodic billiards and infinite translation surfaces

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