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Zbl 0707.58022
Rabinowitz, Paul H.; Tanaka, Kazunaga
Some results on connecting orbits for a class of Hamiltonian systems.
(English)
[J] Math. Z. 206, No.3, 473-499 (1991). ISSN 0025-5874; ISSN 1432-1823/e

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.
[P.H.Rabinowitz]
MSC 2000:
*37J99 Finite-dimensional Hamiltonian etc. systems
58E30 Variational principles on infinite-dimensional spaces

Keywords: connecting orbits; Hamiltonian system

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