Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors

DOI10.1007/BF01049723zbMath0892.58066MaRDI QIDQ1203221

Corrado Falcolini, Rafael de la Llave

Publication date: 26 September 1994

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

zbMATH Keywords

periodic orbitsperturbationPadé approximantsKAM theorysmall divisorsbreakdown of toridomains of analyticityGreen's criterion

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems over complex numbers (37F99)

Related Items (16)

On the singularity structure of invariant curves of symplectic mappings ⋮ Computation of domains of analyticity for some perturbative expansions of mechanics ⋮ Computing (un)stable manifolds with validated error bounds: non-resonant and resonant spectra ⋮ Escape times across the golden cantorus of the standard map ⋮ Numerical Computation of High-Order Expansions of Invariant Manifolds of High-Dimensional Tori ⋮ Accurate computations up to breakdown of quasi-periodic attractors in the dissipative spin-orbit problem ⋮ Numerical integration of high-order variational equations of ODEs ⋮ Computation of domains of analyticity for the dissipative standard map in the limit of small dissipation ⋮ A rigorous partial justification of Greene's criterion ⋮ A renormalization group explanation of numerical observations of analyticity domains ⋮ Numerical Study of Invariant Sets of a Quasiperiodic Perturbation of a Symplectic Map ⋮ Unnamed Item ⋮ Nature of Singularities for Analyticity Domains of Invariant Curves ⋮ Breakdown of Lindstedt expansion for chaotic maps ⋮ An algorithm to generate canonical transformations: Application to normal forms ⋮ Singularities of periodic orbits near invariant curves

Cites Work

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• A rigorous partial justification of Greene's criterion
• Natural boundaries for area-preserving twist maps
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Invariant sets under iteration of rational functions
• On the complex analytic structure of the golden invariant curve for the standard map
• New fixed point of the renormalisation operator associated with the recurrence of invariant circles in generic Hamiltonian maps
• Greene's residue criterion
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