Main Speaker

Adrien Douady

Lessons

1. Sobolev spaces. Decomposition of a function on a simple curve into inner and outer part. Banach manifolds and the implicit functions theorem. The manifold of quadratic-like mappings and that of dynamical annuli.
2. Holomorphic equivalence and Lyubich equivalence. Mating theorems. Inner extension of a dynamical annulus. Circular representative and basic representative. Virtual critical value.
3. Capture theorem. A big diagram of Banach manifolds and foliations. Quasi-conformality of the copy of M in the parameter space of a Mandelbrot-like family.