Canard Cycles and Center Manifolds

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  • Canard Cycles and Center Manifolds Book Detail

  • Author : Freddy Dumortier
  • Release Date : 1996
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 117
  • ISBN 13 : 082180443X
  • File Size : 27,27 MB

Canard Cycles and Center Manifolds by Freddy Dumortier PDF Summary

Book Description: In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon >0$ and for decreasing $a$, the limit cycle created in a Hopf bifurcation at $a = 0$ stays of ``small size'' for a while before it very rapidly changes to ``big size'', representing the typical relaxation oscillation. The authors give a geometric explanation and proof of this phenomenon using foliations by center manifolds and blow-up of unfoldings as essential techniques. The method is general enough to be useful in the study of other singular perturbation problems.

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Canard Cycles and Center Manifolds

Canard Cycles and Center Manifolds

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In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon

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Orders of a Quartic Field

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In this book, the author studies the Dirichlet series whose coefficients are the number of orders of a quartic field with given indices. Nakagawa gives an expli