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＜電子ブック＞
Braids and Dynamics / by Jean-Luc Thiffeault
(Frontiers in Applied Dynamical Systems: Reviews and Tutorials. ISSN:23644931 ; 9)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	XV, 141 p. 71 illus., 37 illus. in color : online resource
著者標目	*Thiffeault, Jean-Luc author SpringerLink (Online service)
件　名	LCSH:Dynamical systems LCSH:Topology FREE:Dynamical Systems FREE:Topology
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-04790-9

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