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.
KeywordsSaddle Point Hamiltonian System Lyapunov Function Phase Portrait Homoclinic Orbit
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