Random Iteration of Rational Functions Page: I
The following text was automatically extracted from the image on this page using optical character recognition software:
Simmons, David. Random Iteration of Rational Functions. Doctor of Philosophy
(Mathematics), May 2012, 143 pp., bibliography, 23 titles.
It is a theorem of Denker and Urbaniski that if T:C-C is a rational map of degree
at least two and if :C--R is Halder continuous and satisfies the "thermodynamic
expanding" condition P(T,) > sup(4), then there exists exactly one equilibrium state p
for T and , and furthermore (C,T,i) 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
Bogenschiitz. Specifically, if (T,Q,P,6) is a holomorphic random dynamical system on C
and Q-- J-k(C) is a Halder continuous random potential function satisfying one of
several sets of technical but reasonable hypotheses, then there exists a unique
equilibrium state of (X,T,4) over (Q,P,6).
Here’s what’s next.
This dissertation can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Dissertation.
Simmons, David. Random Iteration of Rational Functions, dissertation, May 2012; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc115157/m1/2/: accessed July 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .