A criterion for non-existence of invariant tori for Hamiltonian systems

DOI10.1016/0167-2789(89)90248-0zbMath0699.58029OpenAlexW1966704350MaRDI QIDQ913337

Robert S. MacKay

Publication date: 1989

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(89)90248-0

zbMATH Keywords

Hamiltonian systemsinvariant toriinverse KAM theorems

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

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Regions without invariant tori of given class for the planar circular restricted three-body problem ⋮ A continuous family of equilibria in ferromagnetic media are ground states ⋮ On \(C^{1,\beta}\) density of metrics without invariant graphs ⋮ Distinguishing between regular and chaotic orbits of flows by the weighted Birkhoff average ⋮ Periodic and quasi-periodic attractors of weakly-dissipative nearly-integrable systems ⋮ An approximate renormalization for the break-up of invariant tori with three frequencies ⋮ Finding the complement of the invariant manifolds transverse to a given foliation for a 3D flow ⋮ Hamiltonian diffeomorphisms and Lagrangian distributions ⋮ Regions of nonexistence of invariant tori for spin-orbit models ⋮ Nonexistence of invariant tori transverse to foliations: An application of converse KAM theory ⋮ Hamiltonian systems, Lagrangian tori and Birkhoff's theorem

Cites Work

• Converse KAM: theory and practice
• Geodesic flows on the two-dimensional torus and phase transitions ``commensurability-noncommensurability
• Construction of analytic KAM-surfaces and effective stability bounds
• An exhaustive criterion for the non-existence of invariant circles for area-preserving twist maps
• Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures
• KAM theory in configuration space
• Non-existence of invariant circles
• Converse KAM theory for symplectic twist maps
• Monotone twist mappings and the calculus of variations
• Morse Theory. (AM-51)
• 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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