Sergei Yakovenko's blog: on Math and Teaching

Wednesday, November 21, 2007

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

Filed under: Analytic ODE course,lecture — Sergei Yakovenko @ 5:41
Tags: , , , ,

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) .


1 Comment »

  1. Dear Sergei!

    My name is Yaroslav Abramov, I’m a student of the Independent University of Moscow.

    May I interest? Can you give some information (or referrences) about centralizers of formal vector fields? Is this a completely solved problem?

    Will this answer be received on my e-mail?


    Comment by Yarick Abramov — Tuesday, July 7, 2009 @ 10:47 | Reply

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