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Constructing an expanding metric for dynamical systems in one complex variable

Suzanne Lynch Hruska
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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.

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Suzanne Lynch Hruska. 2004-07-22. Constructing an expanding metric for dynamical systems in one complex variable. https://doi.org/10.1088/0951-7715%2F18%2F1%2F005

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