Topological pressure and fractal dimensions for bi-Lipschitz mappings

Authors

Hugo E. Olvera, University of Texas-Pan American

Date of Award

5-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Mrinal Kanti Roychowdhury

Second Advisor

Dr. Timothy Huber

Third Advisor

Dr. Virgil Pierce

Abstract

In this thesis, first we have defined the topological pressure P(t) and then using Banach limit we have determined a unique Borel probability measure µh supported by the invariant set E of a system of bi-Lipschitz mappings where h is the unique zero of the pressure function. Using the topological pressure and the measure µh, under certain condition on bi-Lipschitz constants, we have shown that the fractal dimensions such as the Hausdorff dimension, the packing dimension and the box-counting dimension of the set E are all equal to h. Moreover, it is shown that the h-dimensional Hausdorff measure and the h-dimensional packing measure are finite and positive.

Comments

Copyright 2014 Hugo E. Olvera. All Rights Reserved.

https://www.proquest.com/dissertations-theses/topological-pressure-fractal-dimensions-bi/docview/1560677445/se-2

Granting Institution

University of Texas-Pan American