On hyperbolicity in the renormalization of near-critical area-preserving maps

DOI10.3934/DCDS.2016106zbMath1369.37053OpenAlexW2535934392MaRDI QIDQ727423

Hans Koch

Publication date: 6 December 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2016106

zbMATH Keywords

renormalizationhyperbolicityarea-preserving mapinvariant circle

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Universality and renormalization of dynamical systems (37E20) Renormalization of holomorphic dynamical systems (37F25)

Related Items (4)

Asymptotic scaling and universality for skew products with factors in SL(2,) ⋮ Escape times across the golden cantorus of the standard map ⋮ A functional analytic approach to validated numerics for eigenvalues of delay equations ⋮ Golden mean renormalization for the almost Mathieu operator and related skew products

Uses Software

• Ada95
• MPFR

Cites Work

• The critical renormalization fixed point for commuting pairs of area-preserving maps
• An obstruction method for the destruction of invariant curves
• A rigorous partial justification of Greene's criterion
• Critical Behavior of a KAM surface. I: Empirical results
• Towards an existence proof of MacKay's fixed point
• Hyperbolicity of renormalization of critical circle maps
• A renormalization group fixed point associated with the breakup of golden invariant tori
• Renormalization for golden circles
• A computer-assisted proof of universality for area-preserving maps
• The obstruction criterion for non-existence of invariant circles and renormalization
• Existence of critical invariant tori
• Greene's residue criterion
• Rigidity for infinitely renormalizable area-preserving maps
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