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Entropy, Dimension and Combinatorial Moduli for One-Dimensional Dynamical Systems

The goal of this thesis is to provide a unified framework in which to analyze the dynamics of two seemingly unrelated families of one-dimensional dynamical systems, namely the family of quadratic polynomials and continued fractions. We develop a combinatorial calculus to describe the bifurcation set of both families and prove they are isomorphic. As a corollary, we establish a series of results describing the behavior of entropy as a function of the parameter. One of the most important applications is the relation between the topological entropy of quadratic polynomials and the Hausdorff dimension of sets of external rays landing on principal veins of the Mandelbrot set. / Mathematics

Identiferoai:union.ndltd.org:harvard.edu/oai:dash.harvard.edu:1/11124847
Date30 September 2013
CreatorsTiozzo, Giulio
ContributorsMcMullen, Curtis T.
PublisherHarvard University
Source SetsHarvard University
Languageen_US
Detected LanguageEnglish
TypeThesis or Dissertation
Rightsopen

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