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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 $\left(HS\right)\phantom{\rule{1.em}{0ex}}{q}^{\text{'}\text{'}}+{V}^{\text{'}}\left(q\right)=0$ 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:
 37J99 Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems 58E30 Variational principles on infinite-dimensional spaces
##### Keywords:
connecting orbits; Hamiltonian system
##### References:
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