Geometry of the bifurcations of the normalized reduced Henon–Heiles family

DOI10.1098/rspa.1982.0106zbMath0526.58024OpenAlexW2155120345MaRDI QIDQ3040179

Richard H. Cushman

Publication date: 1982

Published in: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.1982.0106

zbMATH Keywords

reduced phase spacelevel setsHenon-Heiles Hamiltonianmodel of axisymmetric galaxies

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (12)

Calculations of periodic trajectories for the Hénon–Heiles Hamiltonian using the monodromy method ⋮ Normal form, Lie-Poisson structure and reduction for the Henon-Heiles system ⋮ Homoclinic and heteroclinic orbits of reversible vectorfields under perturbation ⋮ Dynamic coupling in Cooker's sloshing experiment with baffles ⋮ A Hopf variables view on the libration points dynamics ⋮ Higher order approximation to the Hill problem dynamics about the libration points ⋮ Dynamics of mechanical systems with polynomial potentials ⋮ The Lissajous transformation. III: Parametric bifurcations ⋮ The Hénon and Heiles Problem in Three Dimensions. ⋮ Reduction of the semisimple \(1:1\) resonance ⋮ Bifurcation Sequences in the Symmetric 1:1 Hamiltonian Resonance ⋮ On perturbed oscillators in 1-1-1 resonance: The case of axially symmetric cubic potentials

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