Natural boundaries for area-preserving twist maps

DOI10.1007/BF01054437zbMath0892.58062OpenAlexW2026803761MaRDI QIDQ1203290

Alessandra Celletti, Corrado Falcolini, Alberto Berretti, Luigi Chierchia

Publication date: 1 September 1994

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01054437

zbMATH Keywords

Padé approximantsKAM theoryinvariant curvesnatural boundariesconservative dynamical systemsarea-preserving twist diffeomorphisms

Mathematics Subject Classification ID

Padé approximation (41A21) Stability theory for smooth dynamical systems (37C75) Dynamical systems over complex numbers (37F99)

Related Items (12)

On the singularity structure of invariant curves of symplectic mappings ⋮ Computation of domains of analyticity for some perturbative expansions of mechanics ⋮ Scaling, perturbative renormalization and analyticity for the standard map and some generalizations ⋮ Breakdown of rotational tori in 2D and 4D conservative and dissipative standard maps ⋮ On the relationship between the Bruno function and the breakdown of invariant tori ⋮ A rigorous partial justification of Greene's criterion ⋮ Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors ⋮ A renormalization group explanation of numerical observations of analyticity domains ⋮ Unnamed Item ⋮ Nature of Singularities for Analyticity Domains of Invariant Curves ⋮ Breakdown of Lindstedt expansion for chaotic maps ⋮ Singularities of periodic orbits near invariant curves

Cites Work

• Unnamed Item
• Hamiltonian maps in the complex plane
• Construction of analytic KAM-surfaces and effective stability bounds
• Non-existence of invariant circles
• On the complex analytic structure of the golden invariant curve for the standard map
• Recent Developments in the Theory of Hamiltonian Systems

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