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

Buffoni, B.; Séré, E.

Commun. Pure Appl. Math. 49, No. 3, 285-305 (1996).

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.

Reviewer: M.Farkas (Budapest)

MSC:

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

Keywords:

quasi-random behavior; conservative systems; ODE systems; homoclinic connection; homoclinic solutions