Dynamics and ``arithmetics of higher genus surface flows

DOI10.4171/icm2022/143arXiv2207.06404OpenAlexW4389817536MaRDI QIDQ6200697

Corinna Ulcigrai

Publication date: 24 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.06404

zbMATH Keywords

linearizationrenormalizationergodic theoryinterval exchange transformationsDiophantine conditionslocally HamiltonianRauzy-Veech inductionarea-preservingflows on surfacesparabolic dynamicsRauzy-Veech cocyclegeneralized interval exchange transformationsmulti-valued Hamiltonian

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Ergodic theorems, spectral theory, Markov operators (37A30) Continued fractions and generalizations (11J70) Dynamical systems involving maps of the interval (37E05) Flows on surfaces (37E35) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hölder regularity of the solutions of the cohomological equation for Roth type interval exchange maps
• Every flat surface is Birkhoff and Oseledets generic in almost every direction
• The Khinchin theorem for interval-exchange transformations
• Absence of mixing in area-preserving flows on surfaces
• Topological and ergodic properties of closed 1-forms with incommensurable periods
• Exponential mixing for the Teichmüller flow
• On the cohomological equation for nilflows
• A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces
• Herman's theory revisited
• La décomposition dynamique et la différentiabilité des feuilletages des surfaces. (The dynamic decomposition and the differentiability of foliations of surfaces)
• A new proof of M. Herman's theorem
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Gauss measures for transformations on the space of interval exchange maps
• Flows on 2-dimensional manifolds. An overview
• Mixing for some classes of special flows over rotations of the circle
• Solutions of the cohomological equation for area-preserving flows on compact surfaces of higher genus
• Invariant distributions and time averages for horocycle flows
• 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
• The Lagrange and Markov spectra from the dynamical point of view
• Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents
• Sur les courbes definies par les équations différentielles à la surface du tore
• Linearization of generalized interval exchange maps
• Slow chaos in surface flows
• Local rigidity for periodic generalised interval exchange transformations
• On disjointness properties of some parabolic flows
• Absence of mixing for smooth flows on genus two surfaces
• Weak mixing for logarithmic flows over interval exchange transformations
• Multiple mixing and parabolic divergence in smooth area-preserving flows on higher genus surfaces
• Lagrange spectra in Teichmüller dynamics via renormalization
• Diophantine properties of iets and general systems: quantitative proximality and connectivity
• Limit theorems for translation flows
• Nondegenerate saddles and nonmixing transformations. II
• Weak mixing in interval exchange transformations of periodic type
• Singularity of the spectrum for smooth area-preserving flows in genus two and translation surfaces well approximated by cylinders
• Diophantine type of interval exchange maps
• Ratner’s property and mild mixing for smooth flows on surfaces
• Shearing and mixing in parabolic flows
• Geodesic flow on the Teichmueller disk of the regular octagon, cutting sequences and octagon continued fractions maps
• A class of special flows over irrational rotations which is disjoint from mixing flows
• The Modular Surface and Continued Fractions
• On Roth type conditions, duality and central Birkhoff sums for i.e.m.
• Affine interval exchange maps with a wandering interval
• Persistence of wandering intervals in self-similar affine interval exchange transformations
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne
• Sur les dynamiques holomorphes non linéarisables et une conjecture de V. I. Arnold
• Affine interval exchange transformations with wandering intervals
• Deviation for interval exchange transformations
• On the self-similarity problem for smooth flows on orientable surfaces
• A smooth mixing flow on a surface with nondegenerate fixed points
• Spectral disjointness of rescalings of some surface flows
• Lebesgue spectrum of countable multiplicity for conservative flows on the torus
• Ergodicity of skew products over linearly recurrent IETs
• Constructions in elliptic dynamics
• Mixing of asymmetric logarithmic suspension flows over interval exchange transformations
• The cohomological equation for Roth-type interval exchange maps
• Bounded type interval exchange maps
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
• Generalizations of theorems on mixing flows with non-degenerate saddle points on a 2-torus
• Interval exchange transformations
• Multiple mixing for a class of conservative surface flows

This page was built for publication: Dynamics and ``arithmetics of higher genus surface flows