Thurston equivalence for rational maps with clusters

Thomas Sharland

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arXiv · 1108.4808

Thurston equivalence for rational maps with clusters

Thomas Sharland

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Abstract

We investigate rational maps with period one and two cluster cycles. Given the definition of a cluster, we show that, in the case where the degree is $d$ and the cluster is fixed, the Thurston class of a rational map is fixed by the combinatorial rotation number $ρ$ and the critical displacement $δ$ of the cluster cycle. The same result will also be proved in the case that the rational map is quadratic and has a period two cluster cycle, but that the statement is no longer true in the higher degree case.

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Thomas Sharland. 2011-08-24. Thurston equivalence for rational maps with clusters. https://arxiv.org/abs/1108.4808

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