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Titlebook: Bifurcations of Planar Vector Fields; Nilpotent Singularit Freddy Dumortier,Robert Roussarie,Henryk Żaładek Book 1991 Springer-Verlag Berli

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期刊全称Bifurcations of Planar Vector Fields
期刊简称Nilpotent Singularit
影响因子2023Freddy Dumortier,Robert Roussarie,Henryk Żaładek
视频video
学科分类Lecture Notes in Mathematics
图书封面Titlebook: Bifurcations of Planar Vector Fields; Nilpotent Singularit Freddy Dumortier,Robert Roussarie,Henryk Żaładek Book 1991 Springer-Verlag Berli
影响因子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.
Pindex Book 1991
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https://doi.org/10.1007/BFb0098353Vector field; bifurcation; differential equation; dynamical systems; integral; ordinary differential equa
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978-3-540-54521-7Springer-Verlag Berlin Heidelberg 1991
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Interview und dokumentarische MethodeIn this work it is shown that, for small β., the system .=., .=±.+α..+.+β.+β..+β.... has at most two limit cycles when α≠(−1/8, ∞)∖{0} (Part II) and also when α<−1/8 (Part III). Part I contains an introduction to the problem, applications of Abelian integrals and some general results.
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Abelian integrals in unfoldings of codimension 3 singular planar vector fields,In this work it is shown that, for small β., the system .=., .=±.+α..+.+β.+β..+β.... has at most two limit cycles when α≠(−1/8, ∞)∖{0} (Part II) and also when α<−1/8 (Part III). Part I contains an introduction to the problem, applications of Abelian integrals and some general results.
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Bifurcations of Planar Vector Fields978-3-540-38433-5Series ISSN 0075-8434 Series E-ISSN 1617-9692
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