Lyapunov Exponents, Entropy and Dimension

PDF Version Also Available for Download.

Description

We consider diffeomorphisms of a compact Riemann Surface. A development of Oseledec's Multiplicative Ergodic Theorem is given, along with a development of measure theoretic entropy and dimension. The main result, due to L.S. Young, is that for certain diffeomorphisms of a surface, there is a beautiful relationship between these three concepts; namely that the entropy equals dimension times expansion.

Creation Information

Williams, Jeremy M. August 2004.

Context

This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 414 times , with 9 in the last month . More information about this thesis can be viewed below.

Who

People and organizations associated with either the creation of this thesis or its content.

Chair

Committee Members

Publisher

Rights Holder

For guidance see Citations, Rights, Re-Use.

  • Williams, J. M.

Provided By

UNT Libraries

With locations on the Denton campus of the University of North Texas and one in Dallas, UNT Libraries serves the school and the community by providing access to physical and online collections; The Portal to Texas History and UNT Digital Libraries; academic research, and much, much more.

Contact Us

What

Descriptive information to help identify this thesis. Follow the links below to find similar items on the Digital Library.

Degree Information

Description

We consider diffeomorphisms of a compact Riemann Surface. A development of Oseledec's Multiplicative Ergodic Theorem is given, along with a development of measure theoretic entropy and dimension. The main result, due to L.S. Young, is that for certain diffeomorphisms of a surface, there is a beautiful relationship between these three concepts; namely that the entropy equals dimension times expansion.

Language

Identifier

Unique identifying numbers for this thesis in the Digital Library or other systems.

Collections

This thesis is part of the following collection of related materials.

UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

What responsibilities do I have when using this thesis?

When

Dates and time periods associated with this thesis.

Creation Date

  • August 2004

Added to The UNT Digital Library

  • Feb. 15, 2008, 3:35 p.m.

Description Last Updated

  • Aug. 13, 2013, 3:24 p.m.

Usage Statistics

When was this thesis last used?

Yesterday: 1
Past 30 days: 9
Total Uses: 414

Interact With This Thesis

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

Williams, Jeremy M. Lyapunov Exponents, Entropy and Dimension, thesis, August 2004; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc4559/: accessed October 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .