Thurston equivalence for rational maps with clusters

Details Thurston equivalence for rational maps with clusters Thurston equivalence for rational maps with clusters

2011-08-24

arxiv.org/abs/1108.4808v1

Mathematics

Dynamical Systems

19 pages

Scientific paper

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 $\rho$ and the critical displacement $\delta$ 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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