Modern Birkhäuser Classics

Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem

Authors: Roussarie, Robert

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  • ISBN 978-3-0348-0717-3
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Softcover $139.00
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  • ISBN 978-3-0348-9778-5
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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. 

- - -

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)

 

About the authors

Robert Roussarie was Professor of Mathematics at the University of Burgundy, France.       

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


Table of contents (6 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-0348-0718-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-7643-5900-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
price for USA
  • ISBN 978-3-0348-0717-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-0348-9778-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem
Authors
Series Title
Modern Birkhäuser Classics
Series Volume
164
Copyright
1998
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0718-0
DOI
10.1007/978-3-0348-0718-0
Hardcover ISBN
978-3-7643-5900-3
Softcover ISBN
978-3-0348-0717-3
Softcover ISBN
978-3-0348-9778-5
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XVII, 206
Additional Information
Originally published as volume 164 in the Progress in Mathematics series
Topics