KAM theory near multiplicity one resonant surfaces in perturbations of a-priori stable Hamiltonian systems

DOI10.1007/BF02677977zbMath0876.58015OpenAlexW4246075860MaRDI QIDQ1356122

Stephen Wiggins, Michael Rudnev

Publication date: 4 June 1997

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02677977

zbMATH Keywords

normal formKAM theorywhiskered toriintegrability on Cantor setsmultiplicity-one resonance surface

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Normal forms for dynamical systems (37G05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (12)

Persistence of degenerate lower dimensional invariant tori with prescribed frequencies in reversible systems ⋮ Response solutions for completely degenerate oscillators under arbitrary quasi-periodic perturbations ⋮ The almost-periodic solutions of the weakly coupled pendulum equations ⋮ Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems ⋮ Dynamics around simple resonant tori in nearly integrable Hamiltonian systems ⋮ Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems ⋮ Lower-dimensional tori in multi-scale, nearly integrable Hamiltonian systems ⋮ Persistence of lower-dimensional hyperbolic invariant tori for generalized Hamiltonian systems ⋮ On lower dimensional invariant tori in reversible systems ⋮ Existence of periodically invariant tori on resonant surfaces for twist mappings ⋮ THE ISOENERGETIC KAM-TYPE THEOREM AT RESONANT CASE fOR NEARLY INTEGRABLE HAMILTONIAN SYSTEMS ⋮ Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter

Cites Work

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• On elliptic lower dimensional tori in Hamiltonian systems
• Nekhoroshev estimates for quasi-convex Hamiltonian systems
• The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
• Integrability of hamiltonian systems on cantor sets
• TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW
• THE MECHANISM OF DESTRUCTION OF RESONANCE TORI OF HAMILTONIAN SYSTEMS
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

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