Institute for Mathematical Sciences
J.H. Hubbard & R. Oberste-Vorth
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.
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