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 language||English (US)|
|Number of pages||46|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - 2008|
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