Chaotic invariant sets of high-dimensional Henon-like maps

High-dimensional Henon-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 Henon-like map s the existence of chaotic invariant sets and the density of homoclinic poi nts and heteroclinic points in them. Our method is motivated by Aubry's "an ti-integrability" concept and is rather different from the traditional tech niques such as horseshoes, transversal homoclinic points and heteroclinic c ycles, and snap-back repellers. (C) 2001 Elsevier Science.