Buffoni, B.; Séré, E. A global condition for quasi-random behavior in a class of conservative systems. (English) Zbl 0860.58027 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) Cited in 33 Documents 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 PDF BibTeX XML Cite \textit{B. Buffoni} and \textit{E. Séré}, Commun. Pure Appl. Math. 49, No. 3, 285--305 (1996; Zbl 0860.58027) Full Text: DOI