Sergei Yakovenko's blog: on Math and Teaching

Thursday, May 1, 2008

Lecture 10 (Thu, May 1st, 2008)

Stokes phenomenon for irregular singularities of linear systems

  1. Irregular singularities: total recall. Formal diagonalizability of non-resonant systems.
  2. Sectorial gauge equivalence: formal, holomorphic, asymptotic series.
  3. Separation rays. Sibuya theorem on sectorial normalization (statement).
  4. Sectorial authomorphisms. Rigidity of the normal form in large sectors.
  5. Stokes matrix cochain and Stokes matrix multipliers as complete invariants of holomorphic classification of irregular singularities.
  6. 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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