McMullen, Curtis2009-12-032009-12-03McMullen, Curtis T. 2009. Ribbon R-trees and holomorphic dynamics on the unit disk. Journal of Topology 2(1): 23-76.1753-84241753-8416http://nrs.harvard.edu/urn-3:HUL.InstRepos:3426328Let {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.en-USJournal Article2009-12-0310.1112/jtopol/jtn032