Singularity of the spectrum for smooth area-preserving flows in genus two and translation surfaces well approximated by cylinders

DOI10.1007/s00220-020-03895-xzbMath1480.37050arXiv1912.10250OpenAlexW3111386871MaRDI QIDQ2658942

Corinna Ulcigrai, Krzysztof Frączek, Adam Kanigowski, Jon Chaika

Publication date: 25 March 2021

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.10250

zbMATH Keywords

Hamiltonian flowssmooth invariant measureBirkhoff sumscompact orientable surfaceshyperelliptic permutation

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (4)

Ergodicity, mixing, Ratner's properties and disjointness for classical flows: on the research of Corinna Ulcigrai ⋮ Dependency of the positive and negative long-time behaviors of flows on surfaces ⋮ New phenomena in deviation of Birkhoff integrals for locally Hamiltonian flows ⋮ Dynamics and ``arithmetics of higher genus surface flows

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