000 03122nam a22004935i 4500
001 978-3-540-38433-5
003 DE-He213
005 20190213151725.0
007 cr nn 008mamaa
008 121227s1991 gw | s |||| 0|eng d
020 _a9783540384335
_9978-3-540-38433-5
024 7 _a10.1007/BFb0098353
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aDumortier, Freddy.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aBifurcations of Planar Vector Fields
_h[electronic resource] :
_bNilpotent Singularities and Abelian Integrals /
_cby Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1991.
300 _aVIII, 232 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1480
505 0 _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.
520 _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.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
700 1 _aRoussarie, Robert.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aSotomayor, Jorge.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aŻaładek, Henryk.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662191552
776 0 8 _iPrinted edition:
_z9783540545217
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1480
856 4 0 _uhttps://doi.org/10.1007/BFb0098353
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11660
_d11660