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Good text for a second course on ODES?

  1. Mar 22, 2006 #1
    I've learned the basic methods of ODEs but I'm looking for a more advanced book, covering things like limit cycles, existence and uniqeness thoerems, phase portraits, and so on.

    Does anyone know of a good book for such topics.
  2. jcsd
  3. Mar 22, 2006 #2
    Perko..."Differential Equations & Dynamical Systems

    divides the book into 4 Chapters:intro, Local, Global and Bifurcation theory...Well written i think. And u can self-learn from that text...its what i did(though i was actulally enrolled in the class).
  4. Mar 22, 2006 #3


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    A Second Course in Elementary Differential Equations
    author: Paul Waltman
    ISBN: 0486434788
    Dover Publications

    Ordinary Differential Equations, by V.I. Arnold. I prefer the following
    (old) edition if available, as it is cheaper, but any one is ok.
    Paperback: 270 pages
    Publisher: The MIT Press (July 15, 1978)
    ISBN: 0262510189

    Lectures on Ordinary Differential Equations
    Witold Hurewicz
    Publisher: Dover Publications
    Series: Dover Phoenix Editions Ser.
  5. Mar 23, 2006 #4
    Thank you both.
  6. Mar 27, 2006 #5


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    As a second course, look at:

    Chaos: An Introduction to Dynamical Systems (Textbooks in Mathematical Sciences S.) by J.A. Yorke, K.T. Alligood, T.D. Sauer

    If you want something more hardcore, go for either:

    Kuznetsov - Elements of Appied Bifurcation Theory


    Gukenheimer and Holmes - Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields

    Both are from Springer.
  7. May 23, 2006 #6
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