Chaotic Invariant Sets of High-Dimensional H´enon-Like Maps1

High-dimensional H´enon-like maps have many applications in the research of spatial chaos and traveling waves of extended systems.Meanwhile, they are of great interest in their own right.The aim of this paper is, by applying the implicit function theorem, to show for high-dimensional H´enon-like maps the existence of chaotic invariant sets and the density of homoclinic points and heteroclinic points in them. Our method is motivated by Aubry’s “anti-integrability” concept and is rather different from the traditional techniques such as horseshoes, transversal homoclinic points and heteroclinic cycles, and snap-back repellers