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Homoclinic trajectories of time dependent Hamiltonian systems. (English) Zbl 0951.37002

Ambrosetti, A. (ed.) et al., Variational and local methods in the study of Hamiltonian systems. Proceedings of the workshop, Trieste, Italy, October 24-28, 1994 and the school, Trieste, Italy, 1994. Singapore: World Scientific. 1-16 (1995).
Consider a time dependent Hamiltonian system with compact configuration manifold \(M\) and phase space \(T^*M= \{(q,p)\mid q\in M\), \(p\in T_q^*M\}\). Under some natural assumptions on the Hamiltonian \(H(q,p,t)\) the author presents a survey of variational methods which provide the existence of homoclinic trajectories of time dependent Hamiltonian systems.
For the entire collection see [Zbl 0936.00033].

MSC:

37B55 Topological dynamics of nonautonomous systems
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
70K44 Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics
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