Overview
- Presents tools for studying local bifurcations of limit cycles in families of planar vector fields
- Provides systematic introduction to classical analytic geometric methods applied to regular limit periodic sets and more recent tools for singular limit sets
- Well-balanced basis for teaching special courses
Part of the book series: Modern Birkhäuser Classics (MBC, volume 164)
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Table of contents (6 chapters)
Keywords
About this book
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.
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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 the recently developed methods. The book, reflecting the current state of the art, can also be used for teaching special courses.
(Mathematical Reviews)
Reviews
"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
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem
Authors: Robert Roussarie
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-3-0348-8798-4
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel 1998
Hardcover ISBN: 978-3-7643-5900-3Published: 19 May 1998
Softcover ISBN: 978-3-0348-0717-3Published: 09 December 2013
eBook ISBN: 978-3-0348-0718-0Published: 26 November 2013
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: XVII, 206
Additional Information: Originally published as volume 164 in the Progress in Mathematics series
Topics: Analysis, Global Analysis and Analysis on Manifolds, Partial Differential Equations, Dynamical Systems and Ergodic Theory