“Auxiliary Lesson” שעור עזר) #5) November 22, 2007

Formal linearization and obstructions. Poincare theorem

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

Reading material: Section 4 from the book (printing disabled).Disclaimer (alas, still required) .