**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

- *PoincarÃ© 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. Taylorâ€™s theorem

4. Implicit function theorem (very important)

5. Linear ODEs

(6. 1-dimensional autonomous nonlinear ODEs)