The critical renormalization fixed point for commuting pairs of area-preserving maps

DOI10.1007/s00220-009-0922-1zbMath1196.37074OpenAlexW2130199393MaRDI QIDQ982433

Hans Koch, Gianni Arioli

Publication date: 6 July 2010

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

Full work available at URL: https://doi.org/10.1007/s00220-009-0922-1

zbMATH Keywords

area-preserving maprenormalization operatorcritical fixed point

Mathematics Subject Classification ID

Universality and renormalization of dynamical systems (37E20)

Related Items

Asymptotic scaling and universality for skew products with factors in SL(2,) ⋮ Existence of Invariant Circles for Infinitely Renormalisable Area-Preserving Maps ⋮ Escape times across the golden cantorus of the standard map ⋮ Choptuik's critical spacetime exists ⋮ Computation of the breakdown of analyticity in statistical mechanics models: Numerical results and a renormalization group explanation ⋮ Some questions looking for answers in dynamical systems ⋮ Renormalization group operators for maps and universal scaling of universal scaling exponents ⋮ The destruction of tori in volume-preserving maps ⋮ Combination laws for scaling exponents and relation to the geometry of renormalization operators ⋮ Renormalization conjecture and rigidity theory for circle diffeomorphisms with breaks ⋮ On hyperbolicity in the renormalization of near-critical area-preserving maps ⋮ Golden mean renormalization for the almost Mathieu operator and related skew products

Uses Software

• Ada95

Cites Work

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• New fixed point of the renormalisation operator associated with the recurrence of invariant circles in generic Hamiltonian maps
• Existence of critical invariant tori
• Higher-order fixed points of the renormalisation operator for invariant circles
• Scaling for a Critical Kolmogorov-Arnold-Moser Trajectory

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