Study Week: Selected textbooks only 14.99 each—eBooks & softcovers on sale! Shop now >>

Graduate Texts in Mathematics

Ergodic Dynamics

From Basic Theory to Applications

Authors: Hawkins, Jane

Free Preview
  • Offers an accessible introduction to the dynamics of ergodic systems
  • Unifies topics across ergodic theory, topological dynamics, complex dynamics, and dynamical systems
  • Explores real-world applications from financial fraud to virus dynamics
  • Illustrates theory through engaging examples, applications, and color graphics
see more benefits

Buy this book

eBook 53,49 €
price for Spain (gross)
  • ISBN 978-3-030-59242-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 67,59 €
price for Spain (gross)
  • ISBN 978-3-030-59241-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.

About the authors

Jane Hawkins is Professor Emerita at the University of North Carolina at Chapel Hill. She obtained her Ph.D. from the University of Warwick, where she studied as a Marshall Scholar. Her research interests are centered on dynamical systems and complex dynamics, including cellular automata and Julia sets. She has taught graduate courses related to the text at Stony Brook University, Cal Tech, Duke and UNC. In addition to supervising more than a dozen Ph.D. and master’s students, Hawkins was an inaugural Fellow of the American Mathematical Society where she has also been active in AMS governance.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook 53,49 €
price for Spain (gross)
  • ISBN 978-3-030-59242-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 67,59 €
price for Spain (gross)
  • ISBN 978-3-030-59241-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Ergodic Dynamics
Book Subtitle
From Basic Theory to Applications
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
289
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-59242-4
DOI
10.1007/978-3-030-59242-4
Hardcover ISBN
978-3-030-59241-7
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIV, 336
Number of Illustrations
14 b/w illustrations, 43 illustrations in colour
Topics