Bifurcation at complex instability

DOI10.1007/BF01227832zbMath0588.70015MaRDI QIDQ3716346

D. C. Heggie

Publication date: 1985

Published in: Celestial Mechanics (Search for Journal in Brave)

zbMATH Keywords

canonical transformationinvariant two-dimensional toriquadratic Hamiltoniancomplex instabilitybifurcation of toriplanetary three body problemreduced system with two degrees of freedomstable family of periodic solutionstwo pairs of characteristic multipliers

Mathematics Subject Classification ID

Three-body problems (70F07) Local and nonlocal bifurcation theory for dynamical systems (37G99) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (8)

THE STRUCTURE AND EVOLUTION OF CONFINED TORI NEAR A HAMILTONIAN HOPF BIFURCATION ⋮ Symmetric Homoclinic Orbits at the Periodic Hamiltonian Hopf Bifurcation ⋮ How Does the Hopf Bifurcation Appear in the Hydrogen Atom in a Circularly Polarized (CP) Microwave Field? ⋮ Hopf bifurcation for the hydrogen atom in a circularly polarized microwave field ⋮ Near rectilinear halo orbits and nearby higher-period dynamical structures: orbital stability and resonance properties ⋮ Motion close to the Hopf bifurcation of the vertical family of periodic orbits of \(L_{4}\) ⋮ On the stability of periodic orbits of high dimensional autonomous Hamiltonian systems ⋮ Chaoticity in the vicinity of complex unstable periodic orbits in galactic type potentials

Cites Work

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• Families of periodic planetary-type orbits in the three-body problem and their stability
• On the relation between resonance and instability in planetary systems
• Numerical study of periodic orbit properties in a dynamical system with three degrees of freedom
• The stability of periodic orbits in the three-body problem

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