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

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

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Title: Entropy, Dimension and Combinatorial Moduli for One-Dimensional Dynamical Systems
Author: Tiozzo, Giulio
Citation: Tiozzo, Giulio. 2013. Entropy, Dimension and Combinatorial Moduli for One-Dimensional Dynamical Systems. Doctoral dissertation, Harvard University.
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Abstract: 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.
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11124847
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