Trees and the Dynamics of Polynomials

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Trees and the Dynamics of Polynomials

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Title: Trees and the Dynamics of Polynomials
Author: McMullen, Curtis T.; DeMarco, Laura G.

Note: Order does not necessarily reflect citation order of authors.

Citation: DeMarco, Laura G., and Curtis T. McMullen. 2008. Trees and the dynamics of polynomials. Annales Scientifiques de l'École Normale Supérieure 41: 337-383.
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Abstract: In this paper we study branched coverings of metrized, simplicial
trees F : T → T which arise from polynomial maps f : C → C with
disconnected Julia sets. We show that the collection of all such trees,
up to scale, forms a contractible space PTD compactifying the moduli
space of polynomials of degree D; that F records the asymptotic
behavior of the multipliers of f; and that any meromorphic family of
polynomials over Δ* can be completed by a unique tree at its central
fiber. In the cubic case we give a combinatorial enumeration of the
trees that arise, and show that PT3 is itself a tree.
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