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Braids and dynamics

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Braids and dynamicsby Jean-Luc Thiffeault.
作者:	Thiffeault, Jean-Luc.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	xv, 141 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Braid theory.
電子資源:	https://doi.org/10.1007/978-3-031-04790-9
ISBN:	9783031047909$q(electronic bk.)

Braids and dynamics
Thiffeault, Jean-Luc.

Braids and dynamics[electronic resource] /by Jean-Luc Thiffeault. - Cham :Springer International Publishing :2022. - xv, 141 p. :ill., digital ;24 cm. - Frontiers in applied dynamical systems: reviews and tutorials,v. 92364-4931 ;. - Frontiers in applied dynamical systems: reviews and tutorials ;v.3..

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.

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.

ISBN: 9783031047909$q(electronic bk.)

Standard No.: 10.1007/978-3-031-04790-9doiSubjects--Topical Terms:

284137
Braid theory.

LC Class. No.: QA612.23 / .T45 2022

Dewey Class. No.: 514.22

Braids and dynamics
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505 0 $a 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.
520 $a 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.
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