The Lissajous transformation. III: Parametric bifurcations

DOI10.1007/BF00051693zbMath0756.70016OpenAlexW2001174079MaRDI QIDQ1186237

Bruce R. Miller

Publication date: 28 June 1992

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00051693

zbMATH Keywords

symmetryintegrabilitynormalizationelliptic oscillatorphase flows

Mathematics Subject Classification ID

Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Local and nonlocal bifurcation theory for dynamical systems (37G99) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

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Cites Work

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• Non-integrability of the fourth-order truncated Toda Hamiltonian
• The Lissajous transformation. II: Normalization
• The Lissajous transformation. IV: Delaunay and Lissajous variables
• Reduction of symplectic manifolds with symmetry
• On the applicability of the third integral of motion
• Geometry of the bifurcations of the normalized reduced Henon–Heiles family