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Some results on connecting orbits for a class of Hamiltonian systems. (English) Zbl 0707.58022
The existence of various kinds of connecting orbits is established for the Hamiltonian system (HS)q '' +V ' (q)=0 as well as its time periodic analogue. For the autonomous case, the main assumption is that V has a global maximum, e.g. at x=0. Variational methods then establish the existence of various kinds of orbits terminating at x=0. For the time dependent case it is assumed that V has a local but not global maximum at x=0 and it is proved that (HS) has a homoclinic orbit emanating from and terminating at 0.
Reviewer: P.H.Rabinowitz

MSC:
37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
58E30Variational principles on infinite-dimensional spaces
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