On the existence of long periodic orbits near the Lyapunov's periodic family in general reasonance cases

DOI10.2996/KMJ/1138036554zbMath0515.70028OpenAlexW2002210763MaRDI QIDQ1052123

Hidekazu Ito

Publication date: 1982

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2996/kmj/1138036554

zbMATH Keywords

periodic orbitsn degrees of freedomassumptions for eigenvalues of coefficient matrix of Hamiltonian vector field at originLyapunov periodic familyprimitive periodsreasonance cases

Mathematics Subject Classification ID

Hamilton's equations (70H05) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Cites Work

• Long periodic solutions near an equilibrium in general resonance cases
• Hopf's bifurcation theorem and the center theorem of Liapunov with resonance cases
• On the periodic motions near a given periodic motion of a dynamical system
• Periodic solutions of arbitrarily long periods in Hamiltonian systems
• A new class of periodic solutions in the restricted three body problem
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
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