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Homoclinics and chaotic behaviour for perturbed second order systems. (English) Zbl 0957.37019

The authors deal with homoclinics and chaotic behaviour for perturbed dynamical systems and partial differential equations. They prove a connection between multiplicity results for homoclinics and the properties of the Melnikov primitive, which is based on a variational approach. The authors do not require any general restriction on the time-dependence of the perturbation such as periodicity, almost periodicity, etc.

MSC:

37C29 Homoclinic and heteroclinic orbits for dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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