“Auxiliary Lesson” שעור עזר) #6) November 29, 2007

Holomorphic normalization

1. Poincaré and Siegel domains. Different types of resonances.
2. Fixed point equation and its linearization.
3. Invertibility of the homological operator.
4. Majorant norm and its properties.
5. Poincaré theorem on holomorphic linearization of vector fields in the Poincaré domain.
6. Further results: Poncare-Dulac polynomial normal form in the Poincare domain. Siegel and Brjuno theorems. Yoccoz counterexample. Divergence dychotomy.
7. Normal forms of the self-maps. Schröder-Kœnigs theorem.

Disclaimer, alas, is still relevant…

Reading: Section 5 from the book (printing disabled).