Thermodynamical Formalism

Thermodynamical formalism is a relatively recent area of pure mathematics owing a lot to some classical notions of thermodynamics. On this thesis we state and prove some of the main results in the area of thermodynamical formalism. The first chapter is an introduction to ergodic theory. Some of the main theorems are proved and there is also a quite thorough study of the topology that arises in Borel probability measure spaces. In the second chapter we introduce the notions of topological pressure and measure theoretic entropy and we state and prove two very important theorems, Shannon-McMillan-Breiman theorem and the Variational Principle. Distance expanding maps and their connection with the calculation of topological pressure cover the third chapter. The fourth chapter introduces Gibbs states and the very important Perron-Frobenius Operator. The fifth chapter establishes the connection between pressure and geometry. Topological pressure is used in the calculation of Hausdorff dimensions. Finally the sixth chapter introduces the notion of conformal measures.

Grantor dc:publisher

University of North Texas

Year dc:date

2004

Author dc:creator

• Chousionis, Vasileios

Contributors dc:contributor

• Urbański, Mariusz
• Alikakos, Nicholas
• Douglass, Matthew

• Measure theory.
• Mathematical physics.
• Thermodynamics.
• dynamical systems
• ergodic theory
• chaos
• conformal measures
• topological pressure

Statement dc:rights

• Public
• Copyright
• Chousionis, Vasileios
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 56607022
https://digital.library.unt.edu/ark:/67531/metadc4631/
ark: ark:/67531/metadc4631

OAI identifier oai:identifier

info:ark/67531/metadc4631