Iso-manifold KAM persistence

DOI10.1016/j.jde.2021.10.059zbMath1481.37068OpenAlexW3217574331MaRDI QIDQ2064318

Xuefeng Zhao, Yong Li

Publication date: 5 January 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2021.10.059

zbMATH Keywords

Riemannian manifoldHamiltonian systemiso-manifold KAM theorem

Mathematics Subject Classification ID

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)

Cites Work

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• Diagonalization of three-dimensional pseudo-Riemannian metrics
• Existence of KAM tori in degenerate Hamiltonian systems
• Invariant tori for nearly integrable Hamiltonian systems with degeneracy
• A quasi-periodic Poincaré's theorem
• Persistence of invariant tori on submanifolds in Hamiltonian systems
• KAM-stable Hamiltonians
• Multiscale KAM theorem for Hamiltonian systems
• Persistence of lower dimensional tori of general types in Hamiltonian systems
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• Partial preservation of frequencies in KAM theory

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