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Abstract
In this paper we develop a combinatorial analytic encoding of the Mandelbrot set M. The encoding is implicit in Yoccoz' proof of local connectivity of M at any Yoccoz parameter, i.e. any at most finitely renormalizable parameter for which all periodic orbits are repelling. Using this encoding we define an explicit combinatorial analytic modelspace, which is sufficiently abstract that it can serve as a gobetween for proving that other sets such as the parabolic Mandelbrot set M_{1} has the same combinatorial structure as M. As an immediate application we use here the combinatorialanalytic model to reprove that the dyadic veins of M are arcs and that more generally any two Yoccoz parameters are joined by a unique ruled (in the sense of DouadyHubbard) arc in M.
Original language  English 

Book series  Fields Institute Communications 
Volume  53 
Pages (fromto)  145176 
Number of pages  32 
ISSN  10695265 
Publication status  Published  2008 
Keywords
 The Mandelbrot set
 Yoccoz Puzzles
 Combinatorial Encoding
Projects
 1 Finished

CODY: Conformal Structures and Dynamics
Petersen, C. L., Branner, B., Henriksen, C., Lomonaco, L. L. A., Deniz, A., Godillon, S. & Kabelka, A.
01/01/2007 → 31/12/2010
Project: Research