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Homoclinics and heteroclinics for a class of conservative singular Hamiltonian systems. (English) Zbl 0887.34044

The authors investigate by variational methods an autonomous Hamiltonian system where the potential has a strict global maximum and a singularity at some point.
They prove the existence of homoclinics which turn \(k\) times around the singularity and infinitely many geometrically distinct homoclinics. Moreover, the existence of a heteroclinic orbit and periodic orbit, and the chaotic behavior on some invariant subsets of the energy level \(\varepsilon\) (small) are given. The techniques used are quite manifold, and useful for the study of singular Hamiltonian systems.
Reviewer: Z.Jing (Beijing)

MSC:

34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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