Persistence of lower dimensional hyperbolic invariant tori for nearly integrable symplectic mappings

DOI10.1007/s12346-014-0117-9zbMath1339.37044OpenAlexW2002533926MaRDI QIDQ489225

Qiaoyan Bi, Junxiang Xu

Publication date: 27 January 2015

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-014-0117-9

zbMATH Keywords

Hamiltonian systemKAM theoremsymplectic mappinghyperbolic invariant tori

Mathematics Subject Classification ID

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

Related Items (5)

Persistence of the hyperbolic lower dimensional non-twist invariant torus in a class of Hamiltonian systems ⋮ A KAM theorem for lower dimensional elliptic invariant tori of nearly integrable symplectic mappings ⋮ Gevrey-smoothness of lower dimensional hyperbolic invariant tori for nearly integrable symplectic mappings ⋮ Existence of periodically invariant tori on resonant surfaces for twist mappings ⋮ Existence of invariant curves for area-preserving mappings under weaker non-degeneracy conditions

Cites Work

• Existence of invariant tori in three-dimensional measure-preserving mappings
• On elliptic lower dimensional tori in Hamiltonian systems
• A note on the KAM theorem for symplectic mappings
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• The hyperbolic invariant tori of symplectic mappings
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
• Integrability of hamiltonian systems on cantor sets
• Existence of invariant tori in volume-preserving diffeomorphisms
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