Syllabus
1) Motivation. Examples of dynamical systems.
2) Parameter dependent dynamical systems. Numerical continuation.
3) Dimensional reduction (singular point, corank, bifurcation equation, Lyapunov-Schmidt reduction).
4) Classification of singular points. Detection of singular points (test functions).
5) Steady states of dynamical systems (asymptotic stability, topological equivalence, Hartman-Grobman theorem). Continuation of branches of steady states, loss of stability.
Annotation
Methods for numerical continuation.