Stability transitions for periodic orbits in Hamiltonian systems

DOI10.1007/BF00247673zbMath0438.70021MaRDI QIDQ1142054

Richard C. Churchill, David L. Rod, Giampiero Pecelli

Publication date: 1980

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

periodic orbitsHill's equationelliptic stabilityMoser coordinatesstability transitions

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Hamilton's equations (70H05)

Related Items (14)

Calculations of periodic trajectories for the Hénon–Heiles Hamiltonian using the monodromy method ⋮ Study of chaos in Hamiltonian systems via convergent normal forms ⋮ Equatorial dynamics of charged particles in planetary magnetospheres ⋮ On the circular Sitnikov problem: the alternation of stability and instability in the family of vertical motions ⋮ Henri Poincaré's neglected ideas ⋮ Spectral asymptotics and Lamé spectrum for coupled particles in periodic potentials ⋮ On averaging, reduction, and symmetry in Hamiltonian systems ⋮ Conservative dynamics: unstable sets for saddle-center loops. ⋮ Two important numbers in the Hénon-Heiles dynamics ⋮ Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level ⋮ The general solution of the Hénon-Heiles problem ⋮ Normal form methods for symbolic creation of approximate solutions of nonlinear dynamical systems ⋮ Classical three rotor problem: Periodic solutions, stability and chaos ⋮ Horseshoes for Singly Thermostated Hamiltonians

Cites Work

• Stability regions for Hill's equation
• Homoclinic orbits in Hamiltonian systems
• Coexistence of stable and random motion
• Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung
• On the ultimate behavior of orbits with respect to an unstable critical point. I: Oscillating, asymptotic, and capture orbits
• Discrete and continuous boundary problems
• On the generalization of a theorem of A. Liapounoff
• Normal modes, uncoupling, and stability for a class of nonlinear oscillators
• Generic Bifurcation of Periodic Points
• On the Stability of Periodic Orbits for Nonlinear Oscillator Systems in Regions Exhibiting Stochastic Behavior
• [https://portal.mardi4nfdi.de/wiki/Publication:5675367 Proof of a conjecture of E. Str�mgren]
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