Scaling properties for the radius of convergence of a Lindstedt series: The standard map

DOI10.1016/S0021-7824(01)80007-6zbMath0942.34038OpenAlexW2013485338MaRDI QIDQ1305121

Alberto Berretti, Guido Gentile

Publication date: 14 August 2000

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-7824(01)80007-6

zbMATH Keywords

rotation numberKAM theorycylinderLindstedt series

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Rate of convergence, degree of approximation (41A25) Parametric resonances for nonlinear problems in mechanics (70K28) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (6)

BIFURCATION CURVES OF SUBHARMONIC SOLUTIONS AND MELNIKOV THEORY UNDER DEGENERACIES ⋮ Complex Brjuno functions ⋮ On the relationship between the Bruno function and the breakdown of invariant tori ⋮ Renormalization group in statistical mechanics and mechanics: gauge symmetries and vanishing beta functions ⋮ Summation of divergent series and Borel summability for strongly dissipative differential equations with periodic or quasiperiodic forcing terms ⋮ Breakdown of Lindstedt expansion for chaotic maps

Cites Work

• Unnamed Item
• Twistless KAM tori
• The Brjuno functions and their regularity properties
• KAM theorem revisited
• On the standard map critical function
• Scaling near resonances and complex rotation numbers for the standard map
• METHODS FOR THE ANALYSIS OF THE LINDSTEDT SERIES FOR KAM TORI AND RENORMALIZABILITY IN CLASSICAL MECHANICS: A review with Some Applications

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