Abstract
AbstractWe investigate rational maps with period-one and period-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 where the rational map is quadratic and has a period-two cluster cycle, and we will also show that the statement is no longer true in the higher-degree case.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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