Trees and the dynamics of polynomials

Laura G. DeMarco*, Curtis T. McMullen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)337-382
Number of pages46
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume41
Issue number3
DOIs
StatePublished - 2008

ASJC Scopus subject areas

  • Mathematics(all)

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