JournalsaihpcVol. 6, No. 5pp. 331–346

Periodic and heteroclinic orbits for a periodic hamiltonian system

  • Paul H. Rabinowitz

    Center for the Mathematical Sciences, University of Wisconsin, Madison, Wisconsin 53706, U.S.A.
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Abstract

Consider the Hamiltonian system:

q\limits^{¨} + \mathrm{V}′(q) = 0

where q = (q1,…, qn) and V is periodic in qi, 1 ≦ i ≦ n. It is known that (★) then possesses at least n + 1 equilibrium solutions. Here we (a) give criteria for V so that (★) has non-constant periodic solutions and (b) prove the existence of multiple heteroclinic orbits joining maxima of V.

Résumé

On considère le système hamiltonien

q\limits^{¨} + \mathrm{V}′(q) = 0

où q = (q1,…, qn) et V est périodique en q. On sait qu’il existe n points d’équilibre au moins. Nous donnons ici des conditions sur V pour que (★) ait des solutions périodiques non constantes et des trajectoires hétéroclines joignant les maxima de V.

Cite this article

Paul H. Rabinowitz, Periodic and heteroclinic orbits for a periodic hamiltonian system. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), no. 5, pp. 331–346

DOI 10.1016/S0294-1449(16)30314-6