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.
Rezensionen / Stimmen
"This book is a very pleasant to read, linking seemingly unrelated topic like braid and fluid dynamics, perhaps a bit easier for a pure mathematician than for an applied one, but still very much enjoyable." (Mauro Artigiani, zbMATH 1509.37003, 2023)
"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)
Produkt-Info
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Zielgruppe
Illustrationen
37
34 s/w Abbildungen, 37 farbige Abbildungen
XV, 141 p. 71 illus., 37 illus. in color.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 9 mm
Gewicht
ISBN-13
978-3-031-04789-3 (9783031047893)
DOI
10.1007/978-3-031-04790-9
Schweitzer Klassifikation
Introduction.- Topological dynamics on the torus.- Stretching with three rods.- Braids.- The Thurston-Nielsen classification.- Topological entropy.- Train tracks.- Dynnikov coordinates.- The braidlab library.- Braids and data analysis.- References.- Appendix: Derivation of Dynnikov update rules.
