Random Iteration of Rational Functions Metadata

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Title

  • Main Title Random Iteration of Rational Functions

Creator

  • Author: Simmons, David
    Creator Type: Personal

Contributor

  • Chair: ski, Mariusz Urba
    Contributor Type: Personal
    Contributor Info: Major Professor
  • Committee Member: Cherry, William
    Contributor Type: Personal
  • Committee Member: Fishman, Lior
    Contributor Type: Personal

Publisher

  • Name: University of North Texas
    Place of Publication: Denton, Texas
    Additional Info: www.unt.edu

Date

  • Creation: 2012-05

Language

  • English

Description

  • Content 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 of Bogenschütz. Specifically, if (T,Ω,P,θ) is a holomorphic random dynamical system on ℂ and ϕ:Ω→ ℋα(ℂ) is a Hölder continuous random potential function satisfying one of several sets of technical but reasonable hypotheses, then there exists a unique equilibrium state of (X,P,ϕ) over (Ω,Ρ,θ).

Subject

  • Keyword: Random dynamics
  • Keyword: complex dynamics
  • Keyword: thermodynamic formalism

Collection

  • Name: UNT Theses and Dissertations
    Code: UNTETD

Institution

  • Name: UNT Libraries
    Code: UNT

Rights

  • Rights Access: public
  • Rights Holder: Simmons, David
  • Rights License: copyright
  • Rights Statement: Copyright is held by the author, unless otherwise noted. All rights Reserved.

Resource Type

  • Thesis or Dissertation

Format

  • Text

Identifier

  • Archival Resource Key: ark:/67531/metadc115157

Degree

  • Academic Department: Department of Mathematics
  • Degree Discipline: Mathematics
  • Degree Level: Doctoral
  • Degree Name: Doctor of Philosophy
  • Degree Grantor: University of North Texas
  • Degree Publication Type: disse

Note