Format:
1 Online-Ressource(XV, 141 p. 71 illus., 37 illus. in color.)
Edition:
1st ed. 2022.
ISBN:
9783031047909
Series Statement:
Frontiers in Applied Dynamical Systems: Reviews and Tutorials 9
Content:
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.
Content:
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.
Additional Edition:
ISBN 9783031047893
Additional Edition:
ISBN 9783031047916
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031047893
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031047916
Additional Edition:
Erscheint auch als Druck-Ausgabe Thiffeault, Jean-Luc Braids and dynamics Cham, Switzerland : Springer, 2022 ISBN 9783031047893
Language:
English
Keywords:
Topologische Dynamik
;
Zopf
;
Flüssiges System
;
Gemisch
;
Oberfläche
;
Pseudo-Anosov-Diffeomorphismus
DOI:
10.1007/978-3-031-04790-9
