On the measure of the KAM-tori in a neighbourhood of a separatrix

DOI10.4213/sm9955eMaRDI QIDQ6639693

A. Medvedev

Publication date: 18 November 2024

Published in: Sbornik: Mathematics (Search for Journal in Brave)

zbMATH Keywords

chaosperturbation theoryseparatricesKAM-theorysystems with small parametermeasure of invariant tori

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Cites Work

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• Explicit estimates on the measure of primary KAM tori
• On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems
• Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions
• Small perturbations of an integrable dynamical system with an integral invariant
• Lagrangian tori near resonances of near-integrable Hamiltonian systems
• Introduction to the Perturbation Theory of Hamiltonian Systems
• The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
• Integrability of hamiltonian systems on cantor sets
• 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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