The solenoid and holomorphic motions for Henon maps Philip Mummert 37F9932H50Henon mapholomorphic motionsolenoidconjugacyunstably connectedhyperbolicBottcher coordinate 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. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3148 10.1512/iumj.2007.56.3148 en Indiana Univ. Math. J. 56 (2007) 2739 - 2762 state-of-the-art mathematics http://iumj.org/access/