Foliations of isonergy surfaces and singularities of curves

DOI10.1134/S1560354708060117zbMath1229.37074arXivnlin/0508004MaRDI QIDQ653002

Vered Rom-Kedar, Milena Radnović

Publication date: 6 January 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0508004

zbMATH Keywords

singularityHamiltonian systemintegrable systembifurcation setLiouville foliationisoenergy manifoldLiouville equivalence

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Nearly integrable Hamiltonian systems, KAM theory (70H08)

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Cites Work

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• Singularities of integrable and near-integrable Hamiltonian systems
• Local and semi-local bifurcations in Hamiltonian dynamical systems. Results and examples
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Nonlinear dynamics in driven, damped sine-Gordon systems
• Generic bifurcation of Hamiltonian systems with symmetry. With an appendix by Jerrold Marsden
• On elliptic lower dimensional tori in Hamiltonian systems
• Symmetry and bifurcations of momentum mappings
• Reduction of symplectic manifolds with symmetry
• Orbits homoclinic to resonances: The Hamiltonian case
• Singular perturbation theory for homoclinic orbits in a class of near- integrable Hamiltonian systems
• A note on focus-focus singularities
• A note on degenerate corank-one singularities of integrable Hamiltonian systems
• Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems
• Chaos near resonance
• A quasi-periodic route to chaos in a near-integrable PDE
• Regular and stochastic motion
• Topology and mechanics. I
• Topology and mechanics. II: The planar \(n\)-body problem
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
• Quasi-periodic motions in families of dynamical systems. Order amidst chaos
• Topology, bifurcations and Liouville classification of Kirchhoff equations with an additional integral of fourth degree
• Resonant tori and instabilities in Hamiltonian systems
• Generic Hamiltonian dynamical systems are neither integrable nor ergodic
• Integrable Hamiltonian system with two degrees of freedom. The topological structure of saturated neighbourhoods of points of focus-focus and saddle-saddle type
• Topology of energy surfaces and existence of transversal Poincaré sections
• The method of loop molecules and the topology of the Kovalevskaya top
• On Energy Surfaces and the Resonance Web
• Vanishing twist near focus–focus points
• Efficient calculation of actions
• Classification of solutions of the forced periodic nonlinear Schrödinger equation
• Bifurcations of normally parabolic tori in Hamiltonian systems
• Near strongly resonant periodic orbits in a Hamiltonian system
• Hierarchy of bifurcations in the truncated and forced nonlinear Schrödinger model
• Averaging methods in nonlinear dynamical systems
• Remarks on the definition of hyperbolic tori of Hamiltonian systems

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