Chaotic invariant sets of high-dimensional Hénon-like maps (Q5956503)

By applying the implicit function theorem, the author shows the existence of chaotic invariant sets and the density of homoclinic points and heteroclinic points in them for high-dimensional Hénon-like maps. The technique is motivated by Aubry's ``anti-integrability'' concept and differs from the traditional approaches like transversal homoclinic points and heteroclinic cycles, horseshoes, and snap-back repellers.