Periodic orbits emanating from a resonant equilibrium

DOI10.1007/BF01231143zbMath0193.25302OpenAlexW2105684070MaRDI QIDQ5588464

Jacques Henrard

Publication date: 1970

Published in: Celestial Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01231143

zbMATH Keywords

mechanics of particles and systems

Related Items (29)

Halo orbits around the collinear points of the restricted three-body problem ⋮ The uniqueness of normal forms via Lie transforms and its applications to Hamiltonian systems ⋮ Unnamed Item ⋮ Normalization of the Hamiltonian near \(L_4\) for small values of \(\mu\) ⋮ Nonlinear oscillations of a Hamiltonian system with two degrees of freedom with 2:1 resonance ⋮ Nonlinear oscillations of a 1:1 resonance Hamiltonian system ⋮ Stability and motion in two degree-of-freedom hamiltonian systems for two-to-one commensurability ⋮ Stability of and motion aboutL 4 at three-to-one commensurability ⋮ A Hopf variables view on the libration points dynamics ⋮ Near-resonances and detuning in classical and quantum mechanics ⋮ Higher order approximation to the Hill problem dynamics about the libration points ⋮ Third and fourth order resonances in Hamiltonian systems ⋮ Normal forms for Hamiltonian systems ⋮ An energy-momentum map for the time-reversal symmetric 1:1 resonance with \(\mathbb Z_2{\times}\mathbb Z_2\) symmetry ⋮ Periodic solutions near a resonant equilibrium of a Hamiltonian system ⋮ Remarks on the existence and the non-existence of some kind of periodic orbits for Hamiltonian systems ⋮ On nonlinear motions of Hamiltonian system in case of fourth order resonance ⋮ Universal unfolding of symmetric resonances ⋮ The \(1:\pm 2\) resonance ⋮ Unnamed Item ⋮ Structure of the centre manifold of the \(L_1\), \(L_2\) collinear libration points in the restricted three-body problem ⋮ On the motions of one near-autonomous Hamiltonian system at a 1:1:1 resonance ⋮ A study of the motions of an autonomous Hamiltonian system at a 1:1 resonance ⋮ On the stability of small quasiperiodic motions in the hamiltonian systems ⋮ Bifurcation Sequences in the Symmetric 1:1 Hamiltonian Resonance ⋮ An extension to resonant cases of Liapunov's theorem concerning the periodic solutions near a Hamiltonian equilibrium ⋮ Bifurcations of triple-periodic orbits ⋮ Lyapunov's center theorem for resonant equilibrium ⋮ Lissajous and halo orbits in the restricted three-body problem

Cites Work

• On the integrals of canonical systems
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• The Trojan Manifold in the System Earth-Moon
• Birkhoff's normalization
• Über eine Klasse infinitesimaler, periodischer Bahnen um die Dreieckslibrationspunkte im problème restreint

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