Persistence of hyperbolic tori in Hamiltonian systems

DOI10.1016/j.jde.2003.10.023zbMath1060.37045OpenAlexW2080507255MaRDI QIDQ1763670

Yong Li, Yingfei Yi

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jde.2003.10.023

zbMATH Keywords

KAM theoryHamiltonian systemInvariant toriHyperbolicity

Mathematics Subject Classification ID

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

Related Items (17)

Persistence of lower dimensional tori of general types in Hamiltonian systems ⋮ Persistence of degenerate hyperbolic lower-dimensional invariant tori in Hamiltonian systems with Bruno’s conditions ⋮ Partial preservation of frequencies and Floquet exponents in KAM theory ⋮ Nekhoroshev and KAM stabilities in generalized Hamiltonian systems ⋮ Partial preservation of frequencies and Floquet exponents of invariant tori in the reversible KAM context 2 ⋮ Persistence of degenerate lower dimensional invariant tori with prescribed frequencies in reversible systems ⋮ A formal KAM theorem for Hamiltonian systems and its application to hyperbolic lower dimensional invariant tori ⋮ The almost-periodic solutions of the weakly coupled pendulum equations ⋮ The hyperbolic invariant tori of symplectic mappings ⋮ Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems ⋮ Invariant hyperbolic tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition ⋮ Existence of 3-dimensional tori for 1D complex Ginzburg-Landau equation via a degenerate KAM theorem ⋮ Persistence of lower dimensional invariant tori on sub-manifolds in Hamiltonian systems ⋮ Existence of whiskered KAM tori of conformally symplectic systems ⋮ Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions ⋮ Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter ⋮ Persistence of multi-dimensional degenerate hyperbolic lower dimensional invariant tori in reversible systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of invariant tori in three-dimensional measure-preserving mappings
• Global bifurcations and chaos. Analytical methods
• Invariant tori for nearly integrable Hamiltonian systems with degeneracy
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• KAM theory in configuration space
• On a partially hyperbolic KAM theorem
• Hyperbolic low-dimensional invariant tori and summations of divergent series
• Persistence of invariant tori on submanifolds in Hamiltonian systems
• KAM-stable Hamiltonians
• Convergent series expansions for quasi-periodic motions
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
• Integrability of hamiltonian systems on cantor sets
• Generalized implicit function theorems with applications to some small divisor problems, I
• Biasymptotic solutions of perturbed integrable Hamiltonian systems
• KAM theory without action-angle variables
• Persistence of invariant tori in generalized Hamiltonian systems
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• The transfer lemma for Graff tori and Arnold diffusion time

This page was built for publication: Persistence of hyperbolic tori in Hamiltonian systems