LEADER 03287nam 2200625 450 001 996466508403316 005 20220912132718.0 010 $a3-540-39150-9 024 7 $a10.1007/BFb0082943 035 $a(CKB)1000000000437496 035 $a(SSID)ssj0000323551 035 $a(PQKBManifestationID)12065011 035 $a(PQKBTitleCode)TC0000323551 035 $a(PQKBWorkID)10300451 035 $a(PQKB)11053453 035 $a(DE-He213)978-3-540-39150-0 035 $a(MiAaPQ)EBC5585230 035 $a(Au-PeEL)EBL5585230 035 $a(OCoLC)1066195631 035 $a(MiAaPQ)EBC6842515 035 $a(Au-PeEL)EBL6842515 035 $a(PPN)155231286 035 $a(EXLCZ)991000000000437496 100 $a20220912d1988 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aGlobal bifurcation of periodic solutions with symmetry /$fBernold Fiedler 205 $a1st ed. 1988. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1988] 210 4$dİ1988 215 $a1 online resource (X, 154 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1309 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-19234-4 327 $aMain results -- No symmetry ? a survey -- Virtual symmetry -- Generic local theory -- Generic global theory -- General global theory -- Applications -- Discussion -- Appendix on genericity. 330 $aThis largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1309 606 $aSingularities (Mathematics) 606 $aNonlinear operators 606 $aBifurcation theory 615 0$aSingularities (Mathematics) 615 0$aNonlinear operators. 615 0$aBifurcation theory. 676 $a515 700 $aFiedler$b Bernold$f1956-$056771 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466508403316 996 $aGlobal bifurcation of periodic solutions with symmetry$978557 997 $aUNISA