On the relationship between the Bruno function and the breakdown of invariant tori

DOI10.1016/S0167-2789(99)00221-3zbMath0957.37057WikidataQ126572497 ScholiaQ126572497MaRDI QIDQ1972885

Alessandro Morbidelli, Elena Lega, Ugo Locatelli, Claude Froeschlé

Publication date: 22 March 2001

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian systemsnumber theoryquasiperiodic motionsbreakdown of torus conditionBruno function

Mathematics Subject Classification ID

Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Uses Software

• Algorithm 719

Cites Work

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• On the role of high order resonances in normal forms and in separatrix splitting
• Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions
• Natural boundaries for area-preserving twist maps
• A proof of the exponentially small transversality of the separatrices for the standard map
• Scaling properties for the radius of convergence of a Lindstedt series: The standard map
• The Brjuno functions and their regularity properties
• On the measure of the structure around the last KAM torus before and after its break-up
• Superexponential stability of KAM tori.
• Numerical investigations of the structure around an invariant KAM torus using the frequency map analysis
• Iteration of analytic functions
• Critical functions for complex analytic maps
• On the complex analytic structure of the golden invariant curve for the standard map
• Greene's residue criterion
• On the standard map critical function
• Algorithm 719: Multiprecision translation and execution of FORTRAN programs
• Scaling law in the standard map critical function. Interpolating Hamiltonian and frequency map analysis
• The critical function for the semistandard map
• Scaling near resonances and complex rotation numbers for the standard map
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• Two-Dimensional Measure-Preserving Mappings

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