Formal linearization and obstructions. Poincare theorem
- Formal equivalence of formal vector fields (total recall)
- (Additive) Resonances
- Poincare formal linearization theorem
- Proof of the Poincare theorem:
- Homological equation
- Commutator with diagonal linear vector field
- Stabilization of the series
- Resonant monomials. Resonant normal form. Poincare–Dulac paradigm.
- Formal classification of formal self-maps. Multiplicative resonances.
- Survey of further results. Formal types of line and planar singularities.