Henon mappings in the complex domain II: projective and inductive limits of polynomials
John Hubbard, Ralph W. Oberste-Vorth
Abstract
Let H: C2 -> C2 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.
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