A version of Thirring’s approach to the Kolmogorov–Arnold–Moser theorem for quadratic Hamiltonians with degenerate twist

DOI10.1063/1.532599zbMath0927.37033arXivchao-dyn/9803005OpenAlexW1659586712MaRDI QIDQ4701524

H. R. Jauslin, Cristel Chandre

Publication date: 21 November 1999

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

Full work available at URL: https://arxiv.org/abs/chao-dyn/9803005

zbMATH Keywords

KAM theoreminvariant toriquadratic Hamiltoniansweakly perturbed Hamiltonian systemsHamiltonians with degenerate twist

Mathematics Subject Classification ID

Hamilton's equations (70H05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems in classical and celestial mechanics (37N05) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items

Renormalization-group analysis for the transition to chaos in Hamiltonian systems ⋮ Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems ⋮ Approximate renormalization with codimension-one fixed point for the break-up of some three-frequency tori

Cites Work

• Twistless KAM tori
• Existence of KAM tori in degenerate Hamiltonian systems
• Effective stability and KAM theory
• A proof of the isoenergetic KAM-theorem from the ``ordinary one
• TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS

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