Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem

Released on by Robert Roussarie
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  • Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem Book Detail

  • Author : Robert Roussarie
  • Release Date : 1998-05-19
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 230
  • ISBN 13 : 9783764359003
  • File Size : 12,12 MB
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Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem by Robert Roussarie PDF Summary

Book 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)

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Planar Dynamical Systems

Planar Dynamical Systems

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In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Cana