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Meanders - Sturm Global Attractors, Seaweed Lie Algebras and Classical Yang-Baxter Equation (Hardcover)
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Meanders - Sturm Global Attractors, Seaweed Lie Algebras and Classical Yang-Baxter Equation (Hardcover)
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This unique book's subject is meanders (connected, oriented,
non-self-intersecting planar curves intersecting the horizontal
line transversely) in the context of dynamical systems. By
interpreting the transverse intersection points as vertices and the
arches arising from these curves as directed edges, meanders are
introduced from the graphtheoretical perspective. Supplementing the
rigorous results, mathematical methods, constructions, and examples
of meanders with a large number of insightful figures, issues such
as connectivity and the number of connected components of meanders
are studied in detail with the aid of collapse and multiple
collapse, forks, and chambers. Moreover, the author introduces a
large class of Morse meanders by utilizing the right and left
one-shift maps, and presents connections to Sturm global
attractors, seaweed and Frobenius Lie algebras, and the classical
Yang-Baxter equation. Contents Seaweed Meanders Meanders Morse
Meanders and Sturm Global Attractors Right and Left One-Shifts
Connection Graphs of Type I, II, III and IV Meanders and the
Temperley-Lieb Algebra Representations of Seaweed Lie Algebras CYBE
and Seaweed Meanders
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