Periodic solutions of Hamiltonian systems. (English) Zbl 0358.70014

Rabinowitz, Paul H.

Commun. Pure Appl. Math. 31, 156-184 (1978).

This paper concerns the existence of periodic solutions of the Hamiltonian system:
\[ \dot p = -H_q, \quad \dot q = H_p. \tag{*} \]
In §1 conditions are given on \(H(p,q)\) for (*) to possess solutions having prescribed energy and in §2 having prescribed period. For the latter case \(H\) is also permitted to depend on \(t\).

Reviewer: Paul H. Rabinowitz

MSC:

70G10	Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
70H05	Hamilton’s equations
34C25	Periodic solutions to ordinary differential equations

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