The cohomological equation for Roth-type interval exchange maps

DOI10.1090/S0894-0347-05-00490-XzbMath1112.37002arXivmath/0403518MaRDI QIDQ5313362

Jean-Christophe Yoccoz, Stefano Marmi, Pierre Moussa

Publication date: 29 August 2005

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

Full work available at URL: https://arxiv.org/abs/math/0403518

zbMATH Keywords

ergodicity renormalization Roth-type interval exchanges theorem of Gottschalk and Hedlund

Mathematics Subject Classification ID

Dynamical systems involving maps of the interval (37E05) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Metric theory of continued fractions (11K50)

Related Items

Relating boundary and interior solutions of the cohomological equation for cocycles by isometries of negatively curved spaces. The Lǐsic case* ⋮ Lengths spectrum of hyperelliptic components ⋮ On the cohomological equation of a linear contraction ⋮ Hölder regularity of the solutions of the cohomological equation for Roth type interval exchange maps ⋮ Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture ⋮ New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant ⋮ A temporal central limit theorem for real-valued cocycles over rotations ⋮ Quantitative shrinking target properties for rotations and interval exchanges ⋮ Invariant distributions for homogeneous flows and affine transformations ⋮ Minimality of the Ehrenfest wind-tree model ⋮ Some arithmetical aspects of renormalization in Teichmüller dynamics: on the occasion of Corinna Ulcigrai winning the Brin Prize ⋮ Weak mixing properties of interval exchange transformations and translation flows ⋮ Deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus 1 ⋮ Exponential mixing for the Teichmüller flow ⋮ Dynamics and geometry of the Rauzy–Veech induction for quadratic differentials ⋮ Diophantine type of interval exchange maps ⋮ On the renormalizations of circle homeomorphisms with several break points ⋮ Linearization of generalized interval exchange maps ⋮ The automorphism group of Rauzy diagrams ⋮ Pseudo-Anosov homeomorphisms on translation surfaces in hyperelliptic components have large entropy ⋮ Parabolic flows renormalized by partially hyperbolic maps ⋮ Rigidity for piecewise smooth circle homeomorphisms and certain GIETs ⋮ A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two ⋮ Structure of \(K\)-interval exchange transformations: induction, trajectories, and distance theorems ⋮ New phenomena in deviation of Birkhoff integrals for locally Hamiltonian flows ⋮ Cocycles over interval exchange transformations and multivalued Hamiltonian flows ⋮ Dynamics and ``arithmetics of higher genus surface flows ⋮ There exists an interval exchange with a non-ergodic generic measure ⋮ Dynamical systems. Abstracts from the workshop held July 11--17, 2021 (hybrid meeting) ⋮ Ends of strata of the moduli space of quadratic differentials ⋮ The set of non-uniquely ergodic \(d\)-IETs has Hausdorff codimension 1/2 ⋮ Ratner’s property and mild mixing for smooth flows on surfaces ⋮ Limit theorems for translation flows ⋮ Rigidity for piecewise smooth homeomorphisms on the circle ⋮ Cardinality of Rauzy classes ⋮ A generalization of the self-dual induction to every interval exchange transformation ⋮ Labeled Rauzy classes and framed translation surfaces ⋮ Every flat surface is Birkhoff and Oseledets generic in almost every direction ⋮ SELF-INVERSES, LAGRANGIAN PERMUTATIONS AND MINIMAL INTERVAL EXCHANGE TRANSFORMATIONS WITH MANY ERGODIC MEASURES ⋮ Full families of generalized interval exchange transformations ⋮ Diophantine approximation on Veech surfaces ⋮ Minimality and the Rauzy – Veech algorithm for interval exchange transformations with flips ⋮ On the self-similarity problem for smooth flows on orientable surfaces ⋮ Simplicity of Lyapunov spectra: a sufficient criterion ⋮ Persistence of wandering intervals in self-similar affine interval exchange transformations ⋮ A spectral cocycle for substitution systems and translation flows ⋮ Hölder regularity for the spectrum of translation flows ⋮ Long hitting time for translation flows and L-shaped billiards ⋮ Ergodic properties of infinite extensions of area-preserving flows ⋮ On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus ⋮ Weak mixing directions in non-arithmetic Veech surfaces ⋮ Multiple mixing and parabolic divergence in smooth area-preserving flows on higher genus surfaces ⋮ RANDOM WALK IN QUASI-PERIODIC RANDOM ENVIRONMENT ⋮ Non-ergodic \(\mathbb{Z}\)-periodic billiards and infinite translation surfaces ⋮ Local rigidity for periodic generalised interval exchange transformations ⋮ Density of mild mixing property for vertical flows of Abelian differentials ⋮ Recognizability for sequences of morphisms ⋮ Khinchin type condition for translation surfaces and asymptotic laws for the Teichmuller flow ⋮ On Selberg’s eigenvalue conjecture for moduli spaces of abelian differentials ⋮ Cohomological equations for linear involutions ⋮ Ruelle spectrum of linear pseudo-Anosov maps ⋮ A Sufficient Condition for Absolute Continuity of Conjugations between Interval Exchange Maps ⋮ Lagrange spectra in Teichmüller dynamics via renormalization ⋮ Weak mixing in interval exchange transformations of periodic type ⋮ Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards ⋮ Sobolev regularity of solutions of the cohomological equation ⋮ Diagonal changes for surfaces in hyperelliptic components ⋮ Twisted cohomological equations for translation flows

Cites Work