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Periodic and heteroclinic orbits for a periodic Hamiltonian system. (English) Zbl 0701.58023

Der Autor betrachtet Hamiltonsche Systeme der Form \((1)\quad \ddot q+V'(q)=0,\) wobei \(q=(q_ 1,...,q_ n)\) und V periodisch in \(q_ i\), \(1\leq i\leq n\), ist. Es werden Kriterien angegeben, unter denen das System (1) nicht konstante periodische Lösungen besitzt, und die Form der Trajektorien in der Nähe von Maxima der Funktion V werden untersucht.
Reviewer: W.Wendt

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37G99 Local and nonlocal bifurcation theory for dynamical systems
34C25 Periodic solutions to ordinary differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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References:

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