Rabinowitz, Paul H. Periodic solutions of Hamiltonian systems. (English) Zbl 0358.70014 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 Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 19 ReviewsCited in 215 Documents 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 PDF BibTeX XML Cite \textit{P. H. Rabinowitz}, Commun. Pure Appl. Math. 31, 156--184 (1978; Zbl 0358.70014) Full Text: DOI OpenURL References: [1] Seifert, Math. Z. 51 pp 197– (1948) [2] Berger, J. Diff. Eq. 10 pp 17– (1971) [3] Gordon, J. Diff. Eq. 10 pp 324– (1971) [4] Clark, Proc. A.M.S. 39 pp 579– (1973) [5] Weinstein, Inv. Math. 20 pp 47– (1973) [6] Moser, Comm. Pure Appl. Math. 29 pp 727– (1976) [7] and , Periodic solutions near an equilibrium of a non-positive definite Hamiltonian system, preprint. [8] Fadell, Inv. Math. [9] Jacobowitz, J. Diff. Eq. 20 pp 37– (1976) [10] Hartman, Amer. J. of Math. [11] Rabinowitz, Comm. Pure Appl. Math. 31 pp 31– (1978) [12] Critical point theory and the minimax principle, Proc. Symp. Pure Math., 15, A.M.S., Providence, R.I., 1970, pp. 185–212. [13] Amann, Math. Ann. 199 pp 55– (1972) [14] Nirenberg, Ann. Scuol. Norm. Sup. Pisa 13 pp 1– (1959) [15] Rabinowitz, Ann. Scuol. Norm. Sup. Pisa. [16] Periodic orbits for convex Hamiltonian systems, preprint. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.