Qualitative Theory of Planar Differential Systems

Released on by Freddy Dumortier
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  • Qualitative Theory of Planar Differential Systems Book Detail

  • Author : Freddy Dumortier
  • Release Date : 2006-10-13
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 309
  • ISBN 13 : 3540329021
  • File Size : 16,16 MB
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Qualitative Theory of Planar Differential Systems by Freddy Dumortier PDF Summary

Book Description: This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.

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