Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems

DOI10.1016/S0167-2789(02)00374-3zbMath1036.70010OpenAlexW2125335636MaRDI QIDQ1597258

Vered Rom-Kedar, Anna Litvak-Hinenzon

Publication date: 12 May 2002

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

Full work available at URL: https://doi.org/10.1016/s0167-2789(02)00374-3

zbMATH Keywords

chaosdegenerate normal stabilityenergy-momenta bifurcation diagramparabolic \(m\)-resonanceparabolic resonant torus

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (7)

Umbilical torus bifurcations in Hamiltonian systems ⋮ Quasi-periodic Hamiltonian pitchfork bifurcation in a phenomenological model with 3 degrees of freedom ⋮ Foliations of isonergy surfaces and singularities of curves ⋮ Hierarchy of bifurcations in the truncated and forced nonlinear Schrödinger model ⋮ Coherent structures and chaotic advection in three dimensions ⋮ Formation of coherent structures by fluid inertia in three-dimensional laminar flows ⋮ On Hamiltonian bifurcations of invariant tori with a Floquet multiplier −1

Cites Work

• On elliptic lower dimensional tori in Hamiltonian systems
• Arnold diffusion: a variational construction
• The quasi-periodic centre-saddle bifurcation
• Dynamical systems III. Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by A. Iacob.
• Multidimensional symplectic separatrix maps
• Chaos near resonance
• Regular and stochastic motion
• Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forced nonlinear Schrödinger equation
• Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems
• Chaotic Hamiltonian dynamics of particle's horizontal motion in the atmosphere.
• A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of \(\mathbb{T}^2\)
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
• Quasi-periodic motions in families of dynamical systems. Order amidst chaos
• Minimal chaos and stochastic webs
• Resonant tori and instabilities in Hamiltonian systems
• Multibump orbits near the anti-integrable limit for Lagrangian systems
• Unbounded growth of energy in nonautonomous Hamiltonian systems
• ACTION INTEGRALS AND ENERGY SURFACES OF THE KOVALEVSKAYA TOP
• Dynamic Bifurcation in Hamiltonian Systems with One Degree of Freedom
• Slow Passage Through a Pitchfork Bifurcation
• Parabolic resonances and instabilities
• 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
• Drift by coupling to an anti-integrable limit
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems