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Braids and dynamics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Braids and dynamicsby Jean-Luc Thiffeault.
Author:	Thiffeault, Jean-Luc.
Published:	Cham :Springer International Publishing :2022.
Description:	xv, 141 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Braid theory.
Online resource:	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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245 1 0 $a Braids and dynamics $h [electronic resource] / $c by Jean-Luc Thiffeault.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xv, 141 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in applied dynamical systems: reviews and tutorials, $x 2364-4931 ; $v v. 9
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.
650 0 $a Braid theory. $3 284137
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650 1 4 $a Dynamical Systems. $3 913342
650 2 4 $a Topology. $3 185965
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830 0 $a Frontiers in applied dynamical systems: reviews and tutorials ; $v v.3. $3 729239
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