Ergodic Dynamics: From Basic Theory to Applications

This textbook provides an accessible introduction to dynamical systems and ergodic theory,with examples ranging from financial fraud to virus dynamics. It covers measurable dynamical systems,attractors,the Perron-Frobenius theorem,invariant measures,topological and measure theoretic entropy,complex dynamics,cellular automata,mixing properties,shift spaces,and toral automorphisms. It assumes a solid grounding in measure theory,topology,and complex analysis and is suitable for readers across pure and applied mathematics.

Format: Hardback
Length: 336 pages
Publication date: 29 January 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook provides a thorough introduction to the fields of dynamical systems and ergodic theory, with a focus on applications and examples throughout. Motivated by real-world scenarios, the author aims to make the subject accessible to readers with an interest in dynamics and ergodic systems.

The book begins by introducing basic concepts such as measurable dynamical systems, attractors, and the ergodic theorems, using simple examples to illustrate these principles. Chapters are modular, allowing readers to select topics of interest. Key highlights include the Perron-Frobenius theorem, which is presented with proof and applications in areas such as Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems, utilizing the von Neumann factor classification. Topological and measure theoretic entropy are discussed, with an algorithmic application to studying the papillomavirus genome.

A chapter on complex dynamics introduces Julia sets and demonstrates their ergodicity for certain maps. Cellular automata are explored as case studies in one and two dimensions, including Conways Game of Life and latent infections of HIV. Other chapters cover mixing properties, shift spaces, and toral automorphisms.

Ergodic Dynamics serves as a unifying text that bridges ergodic theory, topological dynamics, complex dynamics, and dynamical systems. It offers a comprehensive overview of the area, with rich illustrations through examples, real-world connections, and vivid color graphics. The book is suitable for readers with a solid foundation in measure theory, topology, and complex analysis, making it an invaluable resource for both pure and applied mathematics.

Weight: 668g
Dimension: 162 x 241 x 27 (mm)
ISBN-13: 9783030592417
Edition number: 1st ed. 2021