Sergei Yakovenko's blog: on Math and Teaching

Thursday, April 17, 2008

Lecture 9 (Thu, Apr 17, 2008)

Irregular singularities of linear systems

  1. One-dimensional case: complete classification.
  2. Polynomial “normal forms”: Birkhoff theorem and its “uselessness”.
  3. Local reducibility: similarities and differences with the regular (Fuchsian) case.
  4. Polynomial “normal form” for irreducible irregular singularity: Bolibruch theorem
  5. 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: הגדה של פסח

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