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Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing. (English) Zbl 1005.37028

It is known that slowly varying Hamiltonian systems sometimes exhibit very complicated behaviour. The goal of this paper is to show that such systems can have a rich variety of solutions whose behaviour can be described in terms of symbolic coding. To this end the authors use the Conley index theory for fast-slow systems of ODEs. Note that mostly for the study of chaotic dynamics for the time-dependent Hamiltonian systems, one assumes that the Hamiltonian is time periodic, thereby reducing it to the study of the Poincaré map associated to the time period. This approach is not possible here, since the Hamiltonian is not necessarily time periodic.

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
37B10 Symbolic dynamics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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