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Zbl 0955.37040
Tanaka, Kazunaga
Periodic solutions for singular Hamiltonian systems and closed geodesics on non-compact Riemannian manifolds.
(English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 17, No.1, 1-33 (2000). ISSN 0294-1449

The author deals with the so-called prescribed energy problem: $$\ddot q+ \nabla V(q)= 0, \qquad \tfrac 12 |\dot q|^2+ V(q)= H,$$ where $q(t): \bbfR\to \bbfR^N \setminus \{0\}$, $N\geq 2$, $V: \bbfR^n \setminus \{0\}\to \bbfR$ and $H\in \bbfR$. The author studies the existence of periodic solutions of similar Hamiltonian systems as well as the existence of closed geodesics on noncompact Riemannian manifolds in a related situation.
[Messoud Efendiev (Berlin)]
MSC 2000:
*37J45 Periodic, homoclinic and heteroclinic orbits, etc.
58E10 Appl. of bifurcation theory to geodesics
34C25 Periodic solutions of ODE

Keywords: energy problem; Hamiltonian systems; closed geodesics; Riemannian manifold

Cited in: Zbl 0992.53029

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