✦ LIBER ✦

Periodic solutions for singular Hamiltonian systems and closed geodesics on non-compact Riemannian manifolds

✍ Scribed by Kazunaga Tanaka

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 206 KB
Volume: 17
Category: Article
ISSN: 0294-1449
DOI: 10.1016/s0294-1449(99)00102-x

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✦ Synopsis

We study the existence of periodic solutions of singular Hamiltonian systems as well as closed geodesics on non-compact Riemannian manifolds via variational methods.

For Hamiltonian systems, we show the existence of a periodic solution of prescribed-energy problem:

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Let (M, ( } , } ) R ) be a Riemannian manifold and V: M Ä R a C 2 potential function. The research of periodic solutions of the system where D t (x\* (t)) is the covariant derivative of x\* along the direction of x\* and { R the Riemannian gradient, has been studied when M is a noncontractible mani