Examples and Applications of Infinite Iterated Function Systems

The aim of this work is the study of infinite conformal iterated function systems. More specifically, we investigate some properties of a limit set J associated to such system, its Hausdorff and packing measure and Hausdorff dimension. We provide necessary and sufficient conditions for such systems to be bi-Lipschitz equivalent. We use the concept of scaling functions to obtain some result about 1-dimensional systems. We discuss particular examples of infinite iterated function systems derived from complex continued fraction expansions with restricted entries. Each system is obtained from an infinite number of contractions. We show that under certain conditions the limit sets of such systems possess zero Hausdorff measure and positive finite packing measure. We include an algorithm for an approximation of the Hausdorff dimension of limit sets. One numerical result is presented. In this thesis we also explore the concept of positively recurrent function. We use iterated function systems to construct a natural, wide class of such functions that have strong ergodic properties.

Grantor dc:publisher

University of North Texas

Year dc:date

2000

Author dc:creator

• Hanus, Pawel Grzegorz

Contributors dc:contributor

• Urbański, Mariusz
• Mauldin, R. Daniel
• Zamboni, Luca
• Clark, Alex

• Set theory.
• Iterative methods (Mathematics)
• packing measure
• scaling functions
• set theory
• iterated function systems

Statement dc:rights

• Public
• Copyright
• Hanus, Pawel Grzegorz
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 47291552
https://digital.library.unt.edu/ark:/67531/metadc2642/
ark: ark:/67531/metadc2642

OAI identifier oai:identifier

info:ark/67531/metadc2642