- Poincaré and Siegel domains. Different types of resonances.
- Fixed point equation and its linearization.
- Invertibility of the homological operator.
- Majorant norm and its properties.
- Poincaré theorem on holomorphic linearization of vector fields in the Poincaré domain.
- Further results: Poncare-Dulac polynomial normal form in the Poincare domain. Siegel and Brjuno theorems. Yoccoz counterexample.
- Normal forms of the self-maps. Schröder-Kœnigs theorem.
Disclaimer, alas, is still relevant…