Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem

In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asympto...

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Main Author: Roussarie, Robert
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Basel Springer Basel 1998, 1998
Edition:1st ed. 1998
Series:Modern Birkhäuser Classics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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245 0 0 |a Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem  |h Elektronische Ressource  |c by Robert Roussarie 
250 |a 1st ed. 1998 
260 |a Basel  |b Springer Basel  |c 1998, 1998 
300 |a XVII, 206 p  |b online resource 
505 0 |a Preface -- 1 Families of Two-dimensional Vector Fields -- 2 Limit Periodic Sets -- 3 The 0-Parameter Case -- 4 Bifurcations of Regular Limit Periodic Sets -- 5 Bifurcations of Elementary Graphics -- 6 Desingularization Theory and Bifurcation of Non-elementary Limit Periodic Sets -- Bibliography -- Index 
653 |a Ergodic theory 
653 |a Global Analysis and Analysis on Manifolds 
653 |a Mathematical analysis 
653 |a Dynamical Systems and Ergodic Theory 
653 |a Partial Differential Equations 
653 |a Analysis (Mathematics) 
653 |a Manifolds (Mathematics) 
653 |a Partial differential equations 
653 |a Global analysis (Mathematics) 
653 |a Analysis 
653 |a Dynamics 
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989 |b SBA  |a Springer Book Archives -2004 
490 0 |a Modern Birkhäuser Classics 
856 |u https://doi.org/10.1007/978-3-0348-8798-4?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 515 
520 |a In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations.  - - - The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in recently developed methods. The book, reflecting the state of the art, can also be used for teaching special courses. (Mathematical Reviews)