Introduction to Dynamical Systems

  • John Wainwright
Part of the NATO ASI Series book series (NSSB, volume 332)

Abstract

These lecture notes provide an introduction to dynamical systems theory at an advanced undergraduate/graduate level and are intended to serve as a reference for these proceedings. The qualitative behaviour of both linear and non-linear autonomous differential equations is discussed. Particular attention is given to Liapunov stability theory, periodic orbits, limit sets, structural stability, and bifurcation theory, leading up to higher order systems and chaos.

Keywords

Vector Field Periodic Orbit Phase Portrait Solution Curve Linear Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Hirsch, M.W. and Smale, S., 1974, Differential Equations, Dynamical Systems and Linear Algebra, (New York, Academic).MATHGoogle Scholar
  2. [2]
    Guckenheimer, J, and Holmes, P., 1983, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, (New York, Springer).MATHGoogle Scholar
  3. [3]
    Nemytskii, V.V. and Stepanov, V.V., 1960, Qualitative Theory of Differential Equations, (Princeton, Princeton University Press).MATHGoogle Scholar
  4. [4]
    Hale, J.K., 1969, Ordinary Differential Equations, (New York, Wiley).MATHGoogle Scholar
  5. [5]
    Hartman, P., 1982, Ordinary Differential Equations, (New York, Wiley).MATHGoogle Scholar
  6. [6]
    Coddington, E.A. and Levinson, N., 1955, Theory of Ordinary Differential Equations, (New York, McGraw-Hill).MATHGoogle Scholar
  7. [7]
    Lefschetz, S., 1957, Differential Equations: Geometric Theory, (New York, Interscience).MATHGoogle Scholar
  8. [8]
    Andronov, and Pontrijagin, 1937, Doklady Akad. Nauk., 14, 247.Google Scholar
  9. [9]
    Peixoto, M.M., 1962, Topology, 1, 101.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    Hopf, E., 1942, Berichte Math-Phys. KISächs Akad. Wiss. Leipzig, 94, 1Google Scholar
  11. Hopf, E., 1942, Berichte Math-Phys. KI Sächs Akad. Wiss. Leipzig, 95, 3.MathSciNetGoogle Scholar
  12. [11]
    Arnold, V.I., 1973, Ordinary Differential Equations, (New York, Springer).MATHGoogle Scholar
  13. [12]
    Milnor, J., 1985, Commun. Math. Phys., 99, 177.MathSciNetADSMATHCrossRefGoogle Scholar
  14. [13]
    Auslander, J., Bhatia, N.P., and Seibert, P., 1964, Bol. Soc. Mat. Mex., 9, 55.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • John Wainwright
    • 1
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

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