Henon mappings in the complex domain II: projective and inductive limits of polynomials

Abstract

Let H: C^2 -> C^2 be the Henon mapping given by (x,y) --> (p(x) - ay,x). The key invariant subsets are K_+/-, the sets of points with bounded forward images, J_+/- = the boundary of K_+/-, J = the union of J_+ and J_-, and K = the union of K_+ and K_-. In this paper we identify the topological structure of these sets when p is hyperbolic and |a| is sufficiently small, ie, when H is a small perturbation of the polynomial p. The description involves projective and inductive limits of objects defined in terms of p alone.