# Stokes phenomenon for irregular singularities of linear systems

- Irregular singularities: total recall. Formal diagonalizability of non-resonant systems.
- Sectorial gauge equivalence: formal, holomorphic, asymptotic series.
- Separation rays. Sibuya theorem on sectorial normalization (statement).
- Sectorial authomorphisms. Rigidity of the normal form in large sectors.
- Stokes matrix cochain and Stokes matrix multipliers as complete invariants of holomorphic classification of irregular singularities.
- Stokes phenomenon. Realization theorem (Birkhoff). Generic divergence of the formal gauge normalizing transformations.

Recommended reading: Sections **20F-20I** from the Book

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