The solenoid and holomorphic motions for Henon maps

Details The solenoid and holomorphic motions for Henon maps The solenoid and holomorphic motions for Henon maps

2006-11-06

arxiv.org/abs/math/0611147v5

Mathematics

Dynamical Systems

20 pages, 3 figures; minor corrections

Scientific paper

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.

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