Bifurcation of periodic orbits on manifolds and Hamiltonian systems

DOI10.1016/0022-0396(80)90084-4zbMath0476.58016OpenAlexW2079612197MaRDI QIDQ1160473

Matthew Bottkol

Publication date: 1980

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(80)90084-4

zbMATH Keywords

celestial mechanicsinvariant submanifold of periodic orbitslinearized Poincare mapperiodic orbits bifurcating off an invariant manifoldperturbations of Hamiltonian vector fieldssmooth families of perturbations of a Hamiltonian vector field

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Celestial mechanics (70F15) Stability theory for smooth dynamical systems (37C75) Local and nonlocal bifurcation theory for dynamical systems (37G99)

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Cites Work

• Lagrangian submanifolds and Hamiltonian systems
• Counterexamples to the Seifert conjecture and opening closed leaves of foliations
• Bifurcations and Hamilton's principle
• Normal modes for nonlinear Hamiltonian systems
• Morse Theory. (AM-51)
• Symplectic v‐manifolds, periodic orbits of hamiltonian systems, and the volume of certain riemannian manifolds
• Periodic orbits near an equilibrium and a theorem by Alan Weinstein
• Bifurcation of periodic orbits on manifolds, and Hamiltonian systems
• Regularization of kepler's problem and the averaging method on a manifold
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