Sergei Yakovenko's blog: on Math and Teaching

Wednesday, November 14, 2007

“Auxiliary Lesson” שעור עזר) #4) November 15, 2007

Filed under: Analytic ODE course,lecture — Sergei Yakovenko @ 8:43
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Formal series, formal vector fields: Flows and embedding

  1. Formal series algebra \mathbb C[[x_1,\dots,x_n]]. Formal vector fields (derivations) \mathscr D[[\mathbb C^n,0]]. Formal equivalence of vector fields. Truncation. Convergence in the formal algebra  \mathbb C[[x_1,\dots,x_n]].
  2. Formal inverse function theorem. Geometric series.
  3. Integration and formal flow of vector fields. Exponent.
  4. Embedding in the flow. Linear case. Matrix logarithms.
  5. Embedding in the flow and formal logarithms.

Reading Section 3 from the textbook.

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