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Bifurcations of Planar Vector Fields Nilpotent Singularities and Abelian Integrals

The 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 cur...

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Bibliographic Details
Main Authors: Dumortier, Freddy, Roussarie, Robert (Author), Sotomayor, Jorge (Author), Zoladek, Henryk (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1991, 1991
Edition:1st ed. 1991
Series:Lecture Notes in Mathematics
Subjects:
Mathematical Analysis
Analysis
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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100 1 |a Dumortier, Freddy 
245 0 0 |a Bifurcations of Planar Vector Fields  |h Elektronische Ressource  |b Nilpotent Singularities and Abelian Integrals  |c by Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Zoladek 
250 |a 1st ed. 1991 
260 |a Berlin, Heidelberg  |b Springer Berlin Heidelberg  |c 1991, 1991 
300 |a VIII, 232 p  |b online resource 
505 0 |a Definitions 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 
653 |a Mathematical analysis 
653 |a Analysis 
700 1 |a Roussarie, Robert  |e [author] 
700 1 |a Sotomayor, Jorge  |e [author] 
700 1 |a Zoladek, Henryk  |e [author] 
041 0 7 |a eng  |2 ISO 639-2 
989 |b SBA  |a Springer Book Archives -2004 
490 0 |a Lecture Notes in Mathematics 
028 5 0 |a 10.1007/BFb0098353 
856 4 0 |u https://doi.org/10.1007/BFb0098353?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 515 
520 |a The 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 

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