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Random Iteration of Rational Functions

Description: It is a theorem of Denker and Urbański that if T:ℂ→ℂ is a rational map of degree at least two and if ϕ:ℂ→ℝ is Hölder continuous and satisfies the “thermodynamic expanding” condition P(T,ϕ) > sup(ϕ), then there exists exactly one equilibrium state μ for T and ϕ, and furthermore (ℂ,T,μ) is metrically exact. We extend these results to the case of a holomorphic random dynamical system on ℂ, using the concepts of relative pressure and relative entropy of such a system, and the variational principle … more
Date: May 2012
Creator: Simmons, David
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Uniformly de Bruijn Sequences and Symbolic Diophantine Approximation on Fractals

Description: Article expanding the Intrinsic Diophantine approximation on fractals first proposed by K. Mahler (1984). This article describes and develops the theory of infinite de Bruijn sequences and answers questions related to Hausdorff dimension, Diophantine approximation, Dirichlet function, and height function.
Date: April 27, 2018
Creator: Fishman, Lior; Merrill, Keith & Simmons, David
Item Type: Refine your search to only Article
Partner: UNT College of Science
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Badly approximable points on self-affine sponges and the lower Assouad dimension

Description: This article highlights a connection between Diophantine approximation and the lower Assouad dimension by using information about the latter to show that the Hausdorff dimension of the set of badly approximable points that lie in certain non-conformal fractals, known as self-affine sponges, is bounded below by the dynamical dimension of these fractals. The results, which are the first to advance beyond the conformal setting, encompass both the case of Sierpiński sponges/carpets (also known as B… more
Date: June 20, 2017
Creator: Das, Tushar; Fishman, Lior; Simmons, David & Urbański, Mariusz
Item Type: Refine your search to only Article
Partner: UNT College of Science
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