Braids and Dynamics / by Jean-Luc Thiffeault

By:

Thiffeault, Jean-Luc [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Frontiers in Applied Dynamical Systems: Reviews and Tutorials ; 9 | Springer eBook CollectionPublisher: Cham : Springer International Publishing, 2022Publisher: Cham : Imprint: Springer, 2022Edition: 1st ed. 2022Description: 1 Online-Ressource(XV, 141 p. 71 illus., 37 illus. in color.)ISBN:

9783031047909

Subject(s):

Additional physical formats: 9783031047893 | 9783031047916 | Erscheint auch als: 9783031047893 Druck-Ausgabe | Erscheint auch als: 9783031047916 Druck-Ausgabe | Erscheint auch als: Braids and dynamics. Druck-Ausgabe Cham, Switzerland : Springer, 2022. xv, 141 SeitenDOI: DOI: 10.1007/978-3-031-04790-9Online resources:

Summary: 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.Summary: 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.PPN: PPN: 181651537XPackage identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

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