Abstract
Consider the standard family of complex Hénon maps H(x,y)=(p(x)−ay,x), where p is a quadratic polynomial and a is a complex parameter. Let U+ be the set of points that escape to infinity under forward iterations. The analytic structure of the escaping set U+ is well understood from previous work of J. Hubbard and R. Oberste-Vorth as a quotient of (C−D‾)×C by a discrete group of automorphisms Γ isomorphic to Z[1/2]/Z. On the other hand, the boundary J+ of U+ is a complicated fractal object on which the Hénon map behaves chaotically. We show how to extend the group action to S1×C, in order to represent the set J+ as a quotient of S1×C/Γ by an equivalence relation. We analyze this extension for Hénon maps that are perturbations of hyperbolic polynomials with connected Julia set or polynomials with a parabolic fixed point.
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