Discrete symmetric dynamical systems at the main resonances with application to axi-symmetric galaxies

DOI10.1098/rsta.1979.0006zbMath0418.70011OpenAlexW2072599568MaRDI QIDQ3851683

Ferdinand Verhulst

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1098/rsta.1979.0006

zbMATH Keywords

dynamical systemsbifurcationsphase spaceresonancesLagrangian dynamicscelestial mechanicscoupled perturbed oscillatorsstability of periodic solutions of Hamiltonian systems

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Hamilton's equations (70H05) Celestial mechanics (70F15) Lagrange's equations (70H03) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

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Mode-locking in nonlinear rotordynamics ⋮ Internal resonances in nonlinearly-coupled oscillators ⋮ Normal form, Lie-Poisson structure and reduction for the Henon-Heiles system ⋮ Variable mass motion in the Hénon–Heiles system ⋮ Analytic methods to find beating transitions of asymmetric Gaussian beams in GNLS equations ⋮ Dynamical analysis of bounded and unbounded orbits in a generalized Hénon-Heiles system ⋮ Escape regions of a quartic potential ⋮ Structure of the centre manifold of the \(L_1\), \(L_2\) collinear libration points in the restricted three-body problem ⋮ On the detuned 2:4 resonance ⋮ Special Features of Galactic Dynamics ⋮ Periodic orbits of a generalized Hénon–Heiles system

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