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Bifurcations of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals

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Bifurcations of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals - Dumortier, Freddy, and Roussarie, Robert, and Sotomayor, Jorge
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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 ...

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Bifurcations of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals 1991, Springer, Berlin, Heidelberg

ISBN-13: 9783540545217

1991 edition

Trade paperback