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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 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).
Date: May 2012
Creator: Simmons, David
Partner: UNT Libraries

Effects of Discharge Tube Geometry on Plasma Ion Oscillations

Description: This study considers the effect, on plasma ion oscillations, of various lengths of discharge tubes as well as various cross sections of discharge tubes. Four different gases were used in generating the plasma. Gas pressure and discharge voltage and current were varied to obtain a large number of signals. A historical survey is given to familiarize the reader with the field. The experimental equipment and procedure used in obtaining data is given. An analysis of the data obtained is presented along with possible explanations for the observed phenomena. Suggestions for future study are made.
Date: May 1975
Creator: Simmons, David Warren
Partner: UNT Libraries