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Poincaré Maps and Nonautonomous Systems in the Plane

  • Stephen Lynch
Chapter

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.

Keywords

Saddle Point Hamiltonian System Phase Portrait Bifurcation Diagram Unstable Manifold 
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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Copyright information

© Birkhäuser Boston 2010

Authors and Affiliations

  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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