LEADER 03637nam 2200553 450 001 9910485593103321 005 20231204130111.0 010 $a3-030-50570-7 035 $a(CKB)5590000000487559 035 $a(MiAaPQ)EBC6648188 035 $a(Au-PeEL)EBL6648188 035 $a(PPN)25806515X 035 $a(EXLCZ)995590000000487559 100 $a20220603d2021 fy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric configurations of singularities of planar polynomial differential systems $ea global classification in the quadratic case /$fJoan C. Arte?s [et al.] 210 1$aCham, Switzerland :$cBirkha?user,$d[2021] 210 4$dŠ2021 215 $a1 online resource (xii, 699 pages) 311 1 $a3-030-50569-3 320 $aIncludes bibliographical references and index. 327 $aPart I Polynomial differential systems with emphasis on the quadratic ones 1 Introduction 2 Survey of results on quadratic differential systems 3 Singularities of polynomial differential systems 4 Invariants in mathematical classification problems 5 Invariant theory of planar polynomial vector fields 6 Main results on classifications of singularities in QS 7 Classifications of quadratic systems with special singularities Part II 8 QS with finite singularities of total multiplicity at most one 9 QS with finite singularities of total multiplicity two 10 QS with finite singularities of total multiplicity three 11 QS with finite singularities of total multiplicity four 12 Degenerate quadratic systems 13 Conclusions 330 $aThis book addresses the global study of finite and infinite singularities of planar polynomial differential systems, with special emphasis on quadratic systems. While results covering the degenerate cases of singularities of quadratic systems have been published elsewhere, the proofs for the remaining harder cases were lengthier. This book covers all cases, with half of the content focusing on the last non-degenerate ones. The book contains the complete bifurcation diagram, in the 12-parameter space, of global geometrical configurations of singularities of quadratic systems. The authors' results provide - for the first time - global information on all singularities of quadratic systems in invariant form and their bifurcations. In addition, a link to a very helpful software package is included. With the help of this software, the study of the algebraic bifurcations becomes much more efficient and less time-consuming. Given its scope, the book will appeal to specialists on polynomial differential systems, pure and applied mathematicians who need to study bifurcation diagrams of families of such systems, Ph. D. students, and postdoctoral fellows. 606 $aSingularities (Mathematics) 606 $aPolynomials 606 $aDifferential equations 606 $aSingularitats (Matemātica)$2thub 606 $aPolinomis$2thub 606 $aEquacions diferencials$2thub 608 $aLlibres electrōnics$2thub 615 0$aSingularities (Mathematics) 615 0$aPolynomials. 615 0$aDifferential equations. 615 7$aSingularitats (Matemātica) 615 7$aPolinomis 615 7$aEquacions diferencials 676 $a514.746 700 $aArte?s$b Joan C.$f1961-$0501630 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910485593103321 996 $aGeometric configurations of singularities of planar polynomial differential systems$92860565 997 $aUNINA