LEADER 03268nam 2200577 450 001 9910542058103321 005 20230809224041.0 010 $a3-11-053171-2 024 7 $a10.1515/9783110533026 035 $a(CKB)3710000001304857 035 $a(MiAaPQ)EBC4851893 035 $a(DE-B1597)477392 035 $a(OCoLC)987934923 035 $a(DE-B1597)9783110533026 035 $a(Au-PeEL)EBL4851893 035 $a(CaPaEBR)ebr11380738 035 $a(CaONFJC)MIL1008651 035 $a(OCoLC)986177886 035 $a(EXLCZ)993710000001304857 100 $a20170519h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aMeanders $eSturm global attractors, seaweed lie algebras and classical Yang-Baxter equation /$fAnna Karnauhova 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (146 pages) 311 $a3-11-053302-2 311 $a3-11-053147-X 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tPreface -- $t1. Seaweed Meanders -- $t2. Meanders -- $t3. Morse Meanders and Sturm Global Attractors -- $t4. Right and Left One-Shifts -- $t5. Connection Graphs of Type I, II, III and IV -- $t6. Meanders and the Temperley-Lieb Algebra -- $t7. Seaweed Lie Algebras and Seaweed Meanders -- $t8. Classical Yang-Baxter Equation and Seaweed Meanders -- $tSummary in German (Zusammenfassung) -- $tBibliography 330 $aThis 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 606 $aCurves, Algebraic 606 $aAttractors (Mathematics) 606 $aLie algebras 606 $aYang-Baxter equation 615 0$aCurves, Algebraic. 615 0$aAttractors (Mathematics) 615 0$aLie algebras. 615 0$aYang-Baxter equation. 676 $a512 700 $aKarnauhova$b Anna$01193475 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910542058103321 996 $aMeanders$92761330 997 $aUNINA