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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

Mathematics --- Curves, Algebraic. --- Attractors (Mathematics) --- Lie algebras. --- Yang-Baxter equation.

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Mathematical physics --- Quantum field theory --- Quantum groups --- Yang-Baxter equation --- Congresses.

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Ordered algebraic structures --- Vector bundles. --- Curves, Elliptic. --- Yang-Baxter equation. --- Fibrés vectoriels --- Courbes elliptiques --- Yang-Baxter, Équation de --- 51 <082.1> --- Mathematics--Series --- Fibrés vectoriels --- Yang-Baxter, Équation de --- Curves, Elliptic --- Vector bundles --- Yang-Baxter equation --- Baxter-Yang equation --- Factorization equation --- Star-triangle relation --- Triangle equation --- Mathematical physics --- Quantum field theory --- Fiber spaces (Mathematics) --- Elliptic curves --- Curves, Algebraic

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Leonhard Euler (1707–1783) was born in Basel, Switzerland. Euler's formula is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. When its variable is the number pi, Euler's formula evaluates to Euler's identity. On the other hand, the Yang–Baxter equation is considered the most beautiful equation by many scholars. In this book, we study connections between Euler’s formulas and the Yang–Baxter equation. Other interesting sections include: non-associative algebras with metagroup relations; branching functions for admissible representations of affine Lie Algebras; super-Virasoro algebras; dual numbers; UJLA structures; etc.

transcendental numbers --- Euler formula --- Yang–Baxter equation --- Jordan algebras --- Lie algebras --- associative algebras --- coalgebras --- Euler’s formula --- hyperbolic functions --- UJLA structures --- (co)derivation --- dual numbers --- operational methods --- umbral image techniques --- nonassociative algebra --- cohomology --- extension --- metagroup --- branching functions --- admissible representations --- characters --- affine Lie algebras --- super-Virasoro algebras --- nonassociative --- product --- smashed --- twisted wreath --- algebra --- separable --- ideal --- n/a --- Yang-Baxter equation --- Euler's formula

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Yang-Baxter equation. --- Universal enveloping algebras. --- Quantum groups. --- Quantum groups --- Universal enveloping algebras --- Yang-Baxter equation --- 530.19 --- Baxter-Yang equation --- Factorization equation --- Star-triangle relation --- Triangle equation --- Mathematical physics --- Quantum field theory --- Algebras, Universal enveloping --- Enveloping algebras, Universal --- Algebra, Universal --- Jordan algebras --- Lie algebras --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Group theory --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- 530.19 Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc