Robert Roussarie

(Author)

Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem (1998)Hardcover - 1998, 19 May 1998

Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem (1998)
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Part of Series
Modern Birkhäuser Classics
Part of Series
Progress in Mathematics
Part of Series
Modern Birkhauser Classics
Print Length
206 pages
Language
English
Publisher
Birkhauser
Date Published
19 May 1998
ISBN-10
3764359005
ISBN-13
9783764359003

Description

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 the recently developed methods. The book, reflecting the current state of the art, can also be used for teaching special courses.
(Mathematical Reviews)

Product Details

Author:
Robert Roussarie
Book Edition:
1998
Book Format:
Hardcover
Country of Origin:
NL
Date Published:
19 May 1998
Dimensions:
23.39 x 15.6 x 1.42 cm
ISBN-10:
3764359005
ISBN-13:
9783764359003
Language:
English
Location:
Basel
Pages:
206
Publisher:
Weight:
498.95 gm

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