Renormalization for piecewise smooth homeomorphisms on the circle

DOI10.1016/j.anihpc.2012.09.004zbMath1338.37052arXiv1201.1401OpenAlexW3101226575MaRDI QIDQ2450583

Kleyber Cunha, Daniel Smania

Publication date: 14 May 2014

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.1401

zbMATH Keywords

convergencerenormalizationuniversalityinterval exchange transformationshomeomorphisms of the circleRauzy-Veech induction

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Symbolic dynamics (37B10) Dynamical systems involving maps of the interval (37E05) Universality and renormalization of dynamical systems (37E20) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (15)

Robust local Hölder rigidity of circle maps with breaks ⋮ Generic rigidity for circle diffeomorphisms with breaks ⋮ The symplectic structure for renormalization of circle diffeomorphisms with breaks ⋮ On the renormalizations of circle homeomorphisms with several break points ⋮ Teichmüller dynamics, dilation tori and piecewise affine circle homeomorphisms ⋮ Circle homeomorphisms with breaks with no \(C^{2-\nu}\) conjugacy ⋮ Interval rearrangement ensembles ⋮ Rigidity for piecewise smooth circle homeomorphisms and certain GIETs ⋮ A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two ⋮ Rigidity for piecewise smooth homeomorphisms on the circle ⋮ Renormalization conjecture and rigidity theory for circle diffeomorphisms with breaks ⋮ Full families of generalized interval exchange transformations ⋮ C^1-rigidity of circle maps with breaks for almost all rotation numbers ⋮ Renormalization of circle diffeomorphisms with a break-type singularity ⋮ A Sufficient Condition for Absolute Continuity of Conjugations between Interval Exchange Maps

Cites Work

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• Herman's theory revisited
• 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
• The periodic points of renormalization
• Rigidity for piecewise smooth homeomorphisms on the circle
• Échanges d'intervalles et transformations induites
• Smoothness of conjugacies of diffeomorphisms of the circle with rotations
• Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne
• Topological weak-mixing of interval exchange maps
• Interval exchange transformations
• Interval exchange transformations

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