Hamiltonian Systems, Lyapunov Functions, and Stability

  • Stephen Lynch


  • To study Hamiltonian systems in the plane.

  • To investigate stability using Lyapunov functions.


Saddle Point Hamiltonian System Lyapunov Function Phase Portrait Homoclinic Orbit 
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Recommended Reading

  1. 1.
    G. M. Zaslaysky, Physics of Chaos in Hamiltonian Systems, World Scientific, Singapore, 1998.CrossRefGoogle Scholar
  2. 2.
    J. Cronin, Differential Equations: Introduction and Qualitative Theory, Marcel Dekker, New York, 1994.MATHGoogle Scholar
  3. 3.
    J. Moser, Recent developments in the theory of Hamiltonian systems, SIAM Rev., 28-4 (1986), 459-485.Google Scholar
  4. 4.
    M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, New York, 1974.MATHGoogle Scholar
  5. 5.
    V. V. Nemitskii and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton University Press, Princeton, NJ, 1960.Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Stephen Lynch
    • 1
  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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