Renormalization conjecture and rigidity theory for circle diffeomorphisms with breaks

DOI10.1007/s00039-014-0309-0zbMath1321.37041OpenAlexW2037507484WikidataQ123250495 ScholiaQ123250495MaRDI QIDQ484475

Saša Kocić, Konstantin M. Khanin

Publication date: 7 January 2015

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00039-014-0309-0

zbMATH Keywords

rigidity theorycircle diffeomorphisms with breaksrenormalization conjecture

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Universality and renormalization of dynamical systems (37E20) Rotation numbers and vectors (37E45)

Related Items

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 ⋮ Some remarks on the geometry of circle maps with a break point ⋮ On the smoothness of the conjugacy between circle maps with a break ⋮ The Thermodynamic Formalism and the Central Limit Theorem for Stochastic Perturbations of Circle Maps with a Break ⋮ Rigidity for piecewise smooth circle homeomorphisms and certain GIETs ⋮ The rigidity conjecture ⋮ C^1-rigidity of circle maps with breaks for almost all rotation numbers ⋮ Rigidity for a class of generalized interval exchange transformations ⋮ Renormalization of circle diffeomorphisms with a break-type singularity ⋮ The thermodynamic formalism and exponents of singularity of invariant measure of circle maps with a single break ⋮ A Sufficient Condition for Absolute Continuity of Conjugations between Interval Exchange Maps ⋮ Invariant manifolds for non-differentiable operators ⋮ Hausdorff dimension of invariant measure of circle diffeomorphisms with a break point

Cites Work

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• Renormalization of isoenergetically degenerate Hamiltonian flows and associated bifurcations of invariant tori
• Reducibility of skew-product systems with multidimensional Brjuno base flows
• Universal properties of the transition from quasi-periodicity to chaos in dissipative systems
• Robust rigidity for circle diffeomorphisms with singularities
• The critical renormalization fixed point for commuting pairs of area-preserving maps
• Herman's theory revisited
• The universal metric properties of nonlinear transformations
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Feigenbaum-Coullet-Tresser universality and Milnor's hairiness conjecture
• Renormalizations and rigidity theory for circle homeomorphisms with singularities of the break type
• Hyperbolicity of renormalization of critical circle maps
• Quantitative universality for a class of nonlinear transformations
• Linearization of generalized interval exchange maps
• Renormalization horseshoe and rigidity for circle diffeomorphisms with breaks
• An approximate renormalization for the break-up of invariant tori with three frequencies
• Rigidity of critical circle mappings. I
• Rigidity for piecewise smooth homeomorphisms on the circle
• Absence of robust rigidity for circle maps with breaks
• Renormalization for piecewise smooth homeomorphisms on the circle
• Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles
• Smoothness of conjugacies of diffeomorphisms of the circle with rotations
• A renormalization group approach to quasiperiodic motion with Brjuno frequencies
• Renormalization of vector fields and Diophantine invariant tori
• Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne
• C^1-rigidity of circle maps with breaks for almost all rotation numbers
• Renormalization and 3-Manifolds Which Fiber over the Circle
• Rigidity of critical circle mappings II
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• Small denominators. I. Mappings of the circumference onto itself
• Renormalization of Hamiltonians for Diophantine frequency vectors and KAM tori