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Journal of Topology Advance Access originally published online on March 3, 2009
Journal of Topology 2009 2(1):23-76; doi:10.1112/jtopol/jtn032
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© 2009 London Mathematical Society

Ribbon R-trees and holomorphic dynamics on the unit disk

Curtis T. McMullen

Mathematics Department, Harvard University, 1 Oxford Street, Cambridge, MA 02138-2901, USA


  Abstract

Let {Delta} sub C denote the unit disk, viewed as a model for the hyperbolic plane. Under rescaling, {Delta} takes on the appearance of a tree, with an additional ribbon structure coming from the cyclic ordering of its ends.

In this paper, we show that branched coverings of ribbon trees naturally compactify the space of proper holomorphic maps f : ({Delta}, 0) -> ({Delta}, 0), and use the structure of these ribbon trees to describe the limiting moduli of f.

Received December 1, 2007.

2000 Mathematics Subject Classification 37F, 20E08


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