Overview
- Presents principal concepts of topological dynamics as applied to fluid dynamics
- Discusses current applications involving braids from data
- Suitable for graduates, advanced undergraduates, and researchers in pure and applied mathematics
Part of the book series: Frontiers in Applied Dynamical Systems: Reviews and Tutorials (FIADS, volume 9)
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Table of contents (10 chapters)
Keywords
About this book
This monograph uses braids to explore dynamics on surfaces, with an eye towards applications to mixing in fluids. The text uses the particular example of taffy pulling devices to represent pseudo-Anosov maps in practice. In addition, its final chapters also briefly discuss current applications in the emerging field of analyzing braids created from trajectory data. While written with beginning graduate students, advanced undergraduates, or practicing applied mathematicians in mind, the book is also suitable for pure mathematicians seeking real-world examples. Readers can benefit from some knowledge of homotopy and homology groups, but these concepts are briefly reviewed. Some familiarity with Matlab is also helpful for the computational examples.
Reviews
“This short book considers an unusual combination of algebraic topology, dynamics and applications to the mixing of fluids. Probably not many mathematics texts use a taffy puller in a primary example. This one does, and it incorporates interesting connections to dynamics on surfaces, the algebraic topology of braids and applications to mixing. … Several intriguing ideas are presented here very quickly, and it takes some effort to make all the pieces fit together.” (Bill Satzer, MAA Reviews, January 29, 2023)
Authors and Affiliations
Bibliographic Information
Book Title: Braids and Dynamics
Authors: Jean-Luc Thiffeault
Series Title: Frontiers in Applied Dynamical Systems: Reviews and Tutorials
DOI: https://doi.org/10.1007/978-3-031-04790-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Softcover ISBN: 978-3-031-04789-3Published: 06 September 2022
eBook ISBN: 978-3-031-04790-9Published: 05 September 2022
Series ISSN: 2364-4532
Series E-ISSN: 2364-4931
Edition Number: 1
Number of Pages: XV, 141
Number of Illustrations: 34 b/w illustrations, 37 illustrations in colour
Topics: Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Topology