# Irregular singularities of linear systems

- One-dimensional case: complete classification.
- Polynomial “normal forms”: Birkhoff theorem and its “uselessness”.
- Local reducibility: similarities and differences with the regular (Fuchsian) case.
- Polynomial “normal form” for irreducible irregular singularity: Bolibruch theorem
- First steps of the “genuine” normal forms theory.
- Resonances.
- Formal diagonalizability of nonresonant systems
- Divergence of the normalizing transformations

Recommended reading: Section 20 from the Book

# Notice

The next week there will be no classes for this reason. Expect the end of the story on May 1, 2008. In the meantime I wish to everybody חג פסח שמח and merry holidays.

**Recommended reading**: