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Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem by Robert Roussarie

Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem

by Robert Roussarie
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Book cover type: Paperback
  • ISBN13: 9783034897785
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 206
  • Original Price: EUR 49.99
  • Language: English
  • Edition: Softcover Repri
  • Item Weight: 351 grams
  • BISAC Subject(s): General, Mathematical Analysis, and Differential Equations / General

From the Back Cover

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)

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

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