CRM: Centro De Giorgi
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Summer School of Mathematics for Economics and Social Sciences

17 September 2012 - 21 September 2012

Planned Activities

Course main lecturer
Florian Wagner, CeNDEF, University of Amsterdam

Syllabus of the course
- 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)