LEADER 03043nam 2200613 450 001 996466757903316 005 20220915123421.0 010 $a3-540-38433-2 024 7 $a10.1007/BFb0098353 035 $a(CKB)1000000000437080 035 $a(SSID)ssj0000321598 035 $a(PQKBManifestationID)12115905 035 $a(PQKBTitleCode)TC0000321598 035 $a(PQKBWorkID)10279858 035 $a(PQKB)11037717 035 $a(DE-He213)978-3-540-38433-5 035 $a(MiAaPQ)EBC5585387 035 $a(Au-PeEL)EBL5585387 035 $a(OCoLC)1066179068 035 $a(MiAaPQ)EBC6842759 035 $a(Au-PeEL)EBL6842759 035 $a(PPN)155185780 035 $a(EXLCZ)991000000000437080 100 $a20220915d1991 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBifurcations of planar vector fields $enilpotent singularities and Abelian integrals /$fFreddy Dumortier [and three others] 205 $a1st ed. 1991. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1991] 210 4$dİ1991 215 $a1 online resource (VIII, 232 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1480 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-54521-2 311 $a3-540-54521-2 327 $aDefinitions and notations -- Transformation into normal form -- Bifurcations of codimension 1 and 2 -- Elementary properties -- The central rescaling -- Conclusions and discussion of remaining problems -- Abelian integrals in unfoldings of codimension 3 singular planar vector fields. 330 $aThe book reports on recent work by the authors on the bifurcation structure of singular points of planar vector fields whose linear parts are nilpotent. The bifurcation diagrams of the most important codimension-three cases are studied in detail. The results presented reach the limits of what is currently known on the bifurcation theory of planar vector fields. While the treatment is geometric, special analytical tools using abelian integrals are needed, and are explicitly developed. The rescaling and normalization methods are improved for application here. The reader is assumed to be familiar with the elements of Bifurcation and Dynamical Systems Theory. The book is addressed to researchers and graduate students working in Ordinary Differential Equations and Dynamical Systems, as well as anyone modelling complex multiparametric phenomena. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1480 606 $aDifferential equations$xNumerical solutions 606 $aBifurcation theory 615 0$aDifferential equations$xNumerical solutions. 615 0$aBifurcation theory. 676 $a515.35 700 $aDumortier$b Freddy$053294 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466757903316 996 $aBifurcations of planar vector fields$981215 997 $aUNISA