Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorDumortier, Freddy. author
TitleBifurcations of Planar Vector Fields [electronic resource] : Nilpotent Singularities and Abelian Integrals / by Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk ลปaล{130}adek
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1991
Connect tohttp://dx.doi.org/10.1007/BFb0098353
Descript VIII, 232 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram