Poincaré Maps and Nonautonomous Systems in the Plane
Aims and Objectives
• To introduce the theory of Poincaré maps.
• To compare periodic and quasiperiodic behavior.
• To introduce Hamiltonian systems with two degrees of freedom.
• To use Poincaré maps to investigate a nonautonomous system of differential equations.
On completion of this chapter, the reader should be able to
• understand the basic theory of Poincaré maps;
• plot return maps for certain systems;
• use the Poincaré map as a tool for studying stability and bifurcations.
KeywordsSaddle Point Hamiltonian System Phase Portrait Bifurcation Diagram Unstable Manifold
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