Integrability and chaotic attractors. Limit cycles of the Lienard systems. Elastic instabilities: twisted rods. Path and surface following: continuation algorithms.
These notes study the dynamics of iterated holomorphic mappings from a Riemann surface to itself. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry.
This Java Applet can be used for the exploration on two-dimensional analytical defined dynamical systems. The system is defined by a set of two differential equations, which will be evaluated within adjustable regions forming a two-dimensional vector field.