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A global condition for quasi-random behavior in a class of conservative systems. (English) Zbl 0860.58027

In this paper two ODE systems of dimension 4 are considered both having a saddle-focus with a homoclinic connection. Conditions are given under which these Hamiltonian systems have an infinite number of “multibump” homoclinic solutions and their dynamic is chaotic.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
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