Chaotic invariant sets of high-dimensional Henon-like maps

[摘要] 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 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. (C) 2001 Elsevier Science.

[发布日期] 2001-12-01

[关键词] high-dimensional Henon-like maps;chaos;homoclinic points;heteroclinic points;symbolic dynamics