On the Hamiltonian Hopf bifurcations in the 3D Hénon-Heiles family

DOI10.1023/A:1016343317119zbMath1035.37038OpenAlexW1819141834MaRDI QIDQ700807

Jan-Cees van der Meer, Heinz Hanßmann

Publication date: 8 October 2002

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1016343317119

zbMATH Keywords

relative equilibriareductionHamiltonian systemsnormal formsbifurcationstransversalityperturbed harmonic oscillatorHamiltonian Hopf bifurcationHénon-Heiles family

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Normal forms for dynamical systems (37G05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items

Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields ⋮ Periodic orbits of perturbed non-axially symmetric potentials in \(1:1:1\) and \(1:1:2\) resonances ⋮ Normal linear stability of quasi-periodic tori ⋮ Hamiltonian systems with detuned 1:1:2 resonance: manifestation of bidromy ⋮ Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance ⋮ Bifurcations of the Hamiltonian fourfold 1:1 resonance with toroidal symmetry ⋮ THE QUASI-PERIODIC REVERSIBLE HOPF BIFURCATION ⋮ Hamiltonian fourfold \(1:1\) resonance with two rotational symmetries ⋮ Equilibria, stability and Hamiltonian Hopf bifurcation of a gyrostat in an incompressible ideal fluid ⋮ Sensitivity tools vs. Poincaré sections ⋮ On the detuned 2:4 resonance ⋮ Relative equilibria and bifurcations in the generalized van der Waals 4D oscillator ⋮ Bifurcations and monodromy of the axially symmetric \(1:1:-2\) resonance ⋮ Algebraic methods for determining Hamiltonian Hopf bifurcations in three-degree-of-freedom systems ⋮ On perturbed oscillators in 1-1-1 resonance: The case of axially symmetric cubic potentials