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Ergodic dynamics: from basic theory to applications / Jane Hawkins.
Author
Hawkins, Jane, 1954-
[Browse]
Format
Book
Language
English
Published/Created
Cham, Switzerland : Springer Nature Switzerland AG, [2021]
©2021
Description
xiv, 336 pages : illustrations (some color) ; 24 cm.
Availability
Available Online
Springer Nature - Springer Mathematics and Statistics eBooks 2021 English International
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA614.8 .H395 2021
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Details
Subject(s)
Differentiable dynamical systems
[Browse]
Ergodic theory
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Series
Graduate texts in mathematics ; 289.
[More in this series]
Graduate texts in mathematics, 0072-5285 ; 289
[More in this series]
Summary note
This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable entry-point to the dynamics of ergodic systems. Modern and classical applications complement the theory on topics ranging from financial fraud to virus dynamics, offering numerous avenues for further inquiry. Starting with several simple examples of dynamical systems, the book begins by establishing the basics of measurable dynamical systems, attractors, and the ergodic theorems. From here, chapters are modular and can be selected according to interest. Highlights include the Perron-Frobenius theorem, which is presented with proof and applications that include Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems using the von Neumann factor classification. Topological and measure theoretic entropy are illustrated and compared in detail, with an algorithmic application of entropy used to study the papillomavirus genome. A chapter on complex dynamics introduces Julia sets and proves their ergodicity for certain maps. Cellular automata are explored as a series of case studies in one and two dimensions, including Conway's Game of Life and latent infections of HIV. Other chapters discuss mixing properties, shift spaces, and toral automorphisms. Ergodic Dynamics unifies topics across ergodic theory, topological dynamics, complex dynamics, and dynamical systems, offering an accessible introduction to the area. Readers across pure and applied mathematics will appreciate the rich illustration of the theory through examples, real-world connections, and vivid color graphics. A solid grounding in measure theory, topology, and complex analysis is assumed; appendices provide a brief review of the essentials from measure theory, functional analysis, and probability.
Bibliographic references
Includes bibliographical references (pages 325-332) and index.
Contents
Preface
The simplest examples
Dynamical Properties of Measurable Transformations
Attractors in Dynamical Systems
Ergodic Theorems
Mixing Properties of Dynamical Systems
Shift Spaces
Perron-Frobenius Theorem and Some Applications
Invariant Measures
No equivalent invariant measures: Type III maps
Dynamics of Automorphisms of the Torus and Other Groups
An Introduction to Entropy
Complex Dynamics
Maximal Entropy Measures on Julia Sets and a Computer Algorithm
Cellular Automata
Appendix A. Measures on Topological Spaces
Appendix B. Integration and Hilbert Spaces
Appendix C. Connections to Probability Theory
Bibliography
Index.
Show 17 more Contents items
ISBN
9783030592448
3030592448
OCLC
1191214812
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Ergodic dynamics : from basic theory to applications / Jane Hawkins.
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