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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 \((HS)\quad q''+V'(q)=0\) 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

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
58E30 Variational principles in infinite-dimensional spaces
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