Hamiltonian Systems, Lyapunov Functions, and Stability


Aims and Objectives

• To study Hamiltonian systems in the plane.

• To investigate stability using Lyapunov functions.

On completion of this chapter, the reader should be able to

• prove whether a system is Hamiltonian;

• sketch phase portraits of Hamiltonian systems;

• use Lyapunov functions to determine the stability of a critical point;

• distinguish between stability and asymptotic stability.


Saddle Point Hamiltonian System Lyapunov Function Phase Portrait Homoclinic Orbit 


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Copyright information

© Birkhäuser Boston 2010

Authors and Affiliations

  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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