Constructing an expanding metric for dynamical systems in one complex variable
arXiv:math/0406003 · doi:10.1088/0951-7715/18/1/005
Abstract
We describe a rigorous computer algorithm for attempting to construct an explicit, discretized metric for which a complex polynomial map is expansive on a given neighborhood of its Julia set. We show construction of such a metric proves the map is hyperbolic. We also examine the question of whether the algorithm can be improved, and the related question of how to build a metric as close to euclidean as possible. Finally, we give several examples generated with our implementation of this algorithm.
18 pages. 8 figures. Revised version (intro. restructured, some minor clarifications through rest)