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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