The solenoid and holomorphic motions for Henon maps
Dynamical Systems
2007-05-23 v5 Complex Variables
Abstract
The McMullen-Sullivan holomorphic motion for topologically conjugate, complex polynomials with connected Julia set follows level sets of the Bottcher coordinate. The Buzzard-Verma holomorphic motion for hyperbolic, unstably connected, polynomial diffeomorphisms of C^2 follows level sets of the Bedford-Smillie solenoid map. It follows that this solenoid map is a conjugacy for those Henon maps that are perturbations of (one-dimensional) hyperbolic maps with connected Julia set.
Cite
@article{arxiv.math/0611147,
title = {The solenoid and holomorphic motions for Henon maps},
author = {Philip P. Mummert},
journal= {arXiv preprint arXiv:math/0611147},
year = {2007}
}
Comments
20 pages, 3 figures; minor corrections