Course main lecturer
Florian Wagner, CeNDEF, University of Amsterdam

Syllabus of the course
Introduction
- Review of linear theory

Structural stability
- Equivalence classes of linear dynamics
- Differentiable and topological equivalence
- Hartman-Grobman theorem
- Structural stability
- General notion of bifurcation

Codimension one bifurcations of vector fields
- Saddle-node bifurcation
- Normal forms
- Hopf bifurcation
- Invariant manifolds
- Homoclinic and heteroclinic bifurcations
- Symmetry
- Pitchfork bifurcation

Codimension one bifurcations of maps
- Poincaré section
- Saddle-node bifurcation
- Neimark-Sacker bifurcation
- Resonances
- Homoclinic tangencies
- Horseshoes

Introduction to Codimension two bifurcations

The following topics are considered prerequisite for the course

1. Complex numbers
2. Eigenvectors, eigenvalues & diagonalisation
3. Taylor’s theorem
4. Implicit function theorem (very important)
5. Linear ODEs
(6. 1-dimensional autonomous nonlinear ODEs)