On the Hénon and Heiles system in three dimensions: the role of the axial symmetry.

DOI10.1016/S0375-9601(97)00110-2zbMath1043.37509OpenAlexW1985917778MaRDI QIDQ1968231

A. Viartola, Juan Félix San-Juan, Patricia Yanguas, Sebastián Ferrer, Jesús F. Palacián

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(97)00110-2

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Nonlinear dynamics in mechanics (70K99)

Related Items

The Hénon and Heiles Problem in Three Dimensions. ⋮ The Hénon and Heiles Problem in Three Dimensions. ⋮ The reversible umbilic bifurcation

Cites Work

• Unnamed Item
• Unnamed Item
• On averaging, reduction, and symmetry in Hamiltonian systems
• The Lissajous transformation. I: Basics
• The Lissajous transformation. III: Parametric bifurcations
• Regular and chaotic dynamics.
• Stochastic behavior in classical and quantum Hamiltonian systems. Volta memorial conference, Como, 1977
• Topology and mechanics. I
• Motion in the core of a triaxial potential
• Discrete symmetric dynamical systems at the main resonances with application to axi-symmetric galaxies
• VISUALIZING RELATIVE EQUILIBRIA AND BIFURCATIONS BY PAINTING HAMILTONIANS ON PERSONAL COMPUTERS
• Calculations of periodic trajectories for the Hénon–Heiles Hamiltonian using the monodromy method
• Three-Dimensional Isotropic Harmonic Oscillator and SU3
• Canonical transformations depending on a small parameter
• Regularization of kepler's problem and the averaging method on a manifold
• Note on Green’s function in anisotropic elasticity
• Averaging methods in nonlinear dynamical systems