LEADER 03694nam 22006975 450 001 9910132313303321 005 20200629194538.0 010 $a3-319-10777-1 024 7 $a10.1007/978-3-319-10777-6 035 $a(CKB)3710000000306118 035 $a(SSID)ssj0001386367 035 $a(PQKBManifestationID)11814646 035 $a(PQKBTitleCode)TC0001386367 035 $a(PQKBWorkID)11368924 035 $a(PQKB)10827146 035 $a(DE-He213)978-3-319-10777-6 035 $a(MiAaPQ)EBC6287894 035 $a(MiAaPQ)EBC5610756 035 $a(Au-PeEL)EBL5610756 035 $a(OCoLC)898067286 035 $a(PPN)183094344 035 $a(EXLCZ)993710000000306118 100 $a20141108d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBifurcation without Parameters /$fby Stefan Liebscher 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XII, 142 p. 34 illus., 29 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2117 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-10776-3 327 $aIntroduction -- Methods & Concepts -- Cosymmetries -- Codimension One -- Transcritical Bifurcation -- PoincarŽe-Andronov-Hopf Bifurcation -- Application: Decoupling in Networks -- Application: Oscillatory Profiles -- Codimension Two -- egenerate Transcritical Bifurcation -- egenerate Andronov-Hopf Bifurcation -- Bogdanov-Takens Bifurcation -- Zero-Hopf Bifurcation -- Double-Hopf Bifurcation -- Application: Cosmological Models -- Application: Planar Fluid Flow -- Beyond Codimension Two -- Codimension-One Manifolds of Equilibria -- Summary & Outlook. 330 $aTargeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2117 606 $aDifferential equations 606 $aDifferential equations, Partial 606 $aDynamics 606 $aErgodic theory 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 615 0$aDifferential equations. 615 0$aDifferential equations, Partial. 615 0$aDynamics. 615 0$aErgodic theory. 615 14$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 615 24$aDynamical Systems and Ergodic Theory. 676 $a515.352 700 $aLiebscher$b Stefan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0716388 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910132313303321 996 $aBifurcation without parameters$91388113 997 $aUNINA