Lecturer:
Andrea Tellini (Universidad Politécnica de Madrid)

Board Contact:
Guglielmo Feltrin

1. Introduction: motivation and examples of continuation and bifurcation theory. Review of required results in calculus, like the implicit function theorem.
2. Crandall-Rabinowitz local bifurcation theorem. Examples.
3. Rabinowitz global alternative. Examples.
4. Theoretical aspects in numerical continuation methods: pseudo arc-length parametrization and continuation at regular points, singular points and determination of bifurcation directions.