Non-degeneracy conditions in KAM theory

DOI10.1016/j.indag.2011.09.005zbMath1253.37058OpenAlexW2112187946MaRDI QIDQ652424

Heinz Hanßmann

Publication date: 14 December 2011

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.indag.2011.09.005

zbMATH Keywords

persistenceKAM theoryinvariant torinon-degeneracy

Mathematics Subject Classification ID

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

Related Items (4)

Whitney smooth families of invariant tori within the reversible context 2 of KAM theory ⋮ Partial preservation of frequencies and Floquet exponents of invariant tori in the reversible KAM context 2 ⋮ Unnamed Item ⋮ Perturbations of superintegrable systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character
• A parametrised version of Moser's modifying terms theorem
• Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum
• Umbilical torus bifurcations in Hamiltonian systems
• Local and semi-local bifurcations in Hamiltonian dynamical systems. Results and examples
• Normal linear stability of quasi-periodic tori
• The reversible umbilic bifurcation
• Quasi-periodic stability of normally resonant tori
• Reversible systems
• On elliptic lower dimensional tori in Hamiltonian systems
• A normally elliptic Hamiltonian bifurcation
• Perturbations of lower dimensional tori for Hamiltonian systems
• Nearly integrable infinite-dimensional Hamiltonian systems
• Unfoldings of quasi-periodic tori in reversible systems
• Persistence of elliptic lower dimensional invariant tori for small perturbation of degenerate integrable Hamiltonian systems
• On Melnikov's persistency problem
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition
• KAM à la R
• Quasi-periodic bifurcations in reversible systems
• Convergent series expansions for quasi-periodic motions
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
• Quasi-periodic motions in families of dynamical systems. Order amidst chaos
• A proof of the isoenergetic KAM-theorem from the ``ordinary one
• Stable and Random Motions in Dynamical Systems
• Integrability of hamiltonian systems on cantor sets
• THE QUASI-PERIODIC REVERSIBLE HOPF BIFURCATION
• Generalized implicit function theorems with applications to some small divisor problems, I
• Generalized implicit function theorems with applications to some small divisor problems, II
• Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach
• Normal Form of Reversible Systems and Persistence of Lower Dimensional Tori under Weaker Nonresonance Conditions
• Unicity of KAM tori
• Geometry of KAM tori for nearly integrable Hamiltonian systems
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• Unfoldings and bifurcations of quasi-periodic tori
• Invariant manifolds
• Lie groups

This page was built for publication: Non-degeneracy conditions in KAM theory