August/September
- Introduction/examples
- Implicit function theorem/big O notation
- Saddle-node bifurcation
- Continuity of eigenvalues
- Lyapunov–Schmidt reduction
- Center manifold reduction
- Center-stable and center-unstable manifolds, genericity saddle-node, regularity issues in center manifolds (Tiago, 22 sep)
- Normal form reduction
October
- Normal form reduction: basics
- Preparation student seminars
- Preparation student seminars
- Guest lecture Tiago: graph transform
- Normal form reduction: infinite order, bifurcation parameters
- Normal form reduction: the transpose method
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November
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Homework
To appear soon
Lecture notes
handwritten
Literature
- Bifurcation Theory by Ale Jan Homburg and Jürgen Knobloch
- Centre Manifolds, Normal Forms and Elementary Bifurcations by A. Vanderbauwhede
- Methods of Qualitative Theory in Nonlinear Dynamics (Part I) by L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev, and L. O. Chua
- Lectures on Dynamical Systems by O. Lanford
- Stable mappings and their singularities by M. Golubitsky and V. Guillemin
- Ordinary Differential Equations with Applications by C. Chicone
- Singularities and groups in bifurcation theory, Vol 1, by M. Golubitsky and D. G. Schaeffer
- Differential Topology by M. W. Hirsch
See also
Tiago Pereira's page on the course in previous years