Hamiltonian fourfold \(1:1\) resonance with two rotational symmetries

DOI10.1134/S1560354707060081zbMath1229.37053MaRDI QIDQ655301

Sebastián Ferrer, Jan-Cees van der Meer, Jose A. Egea

Publication date: 3 January 2012

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

zbMATH Keywords

bifurcationreductionnormal formHamiltonian systemHamiltonian Hopf bifurcationfourfold \(1:1\) resonance

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Hamilton's equations (70H05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items

Reduced 4D oscillators and orbital elements in Keplerian systems: Cushman-Deprit coordinates, Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance, Generalized Hopf fibration and geometric \(\mathrm{SO}(3)\) reduction of the \(4\mathrm{DOF}\) harmonic oscillator, Bifurcations of the Hamiltonian fourfold 1:1 resonance with toroidal symmetry, Poisson and symplectic reductions of 4–DOF isotropic oscillators. The van der Waals system as benchmark, Alternative Reduction by Stages of Keplerian Systems. Positive, Negative, and Zero Energy, Relative equilibria and bifurcations in the generalized van der Waals 4D oscillator, The Kepler system as a reduced 4D harmonic oscillator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Hamiltonian Hopf bifurcations in the 3D Hénon-Heiles family
• The Hamiltonian Hopf bifurcation
• Constrained normalization of Hamiltonian systems and perturbed Keplerian motion
• On perturbed oscillators in 1-1-1 resonance: The case of axially symmetric cubic potentials
• Metamorphoses of Hamiltonian systems with symmetries
• The Keplerian regime of charged particles in planetary magnetospheres
• Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields
• Hamiltonian oscillators in \(1\)-\(1\)-\(1\) resonance: Normalization and integrability
• Algebraic methods for determining Hamiltonian Hopf bifurcations in three-degree-of-freedom systems
• Singular reduction of axially symmetric perturbations of the isotropic harmonic oscillator
• The Hénon and Heiles Problem in Three Dimensions.
• The Hénon and Heiles Problem in Three Dimensions.
• Perturbation theory of Kepler motion based on spinor regularization.
• Regularization of kepler's problem and the averaging method on a manifold