IUMJ

Title: The solenoid and holomorphic motions for Henon maps

Authors: Philip P. Mummert

Issue: Volume 56 (2007), Issue 6, 2739-2762

Abstract:

The McMullen-Sullivan holomorphic motion for topologically conjugate, complex polynomials with connected Julia set follows level sets of the B\"ottcher coordinate. The Buzzard-Verma holomorphic motion for hyperbolic, unstably connected, polynomial diffeomorphisms of $\mathbb{C}^2$ follows level sets of the Bedford-Smillie solenoid map. It follows that this solenoid map is a conjugacy for those H\'enon maps that are perturbations of (one-dimensional) hyperbolic maps with connected Julia set.