## Formal series, formal vector fields: Flows and embedding

- Formal series algebra . Formal vector fields (derivations) . Formal equivalence of vector fields. Truncation. Convergence in the formal algebra .
- Formal inverse function theorem. Geometric series.
- Integration and formal flow of vector fields. Exponent.
- Embedding in the flow. Linear case. Matrix logarithms.
- Embedding in the flow and formal logarithms.

Reading Section 3 from the textbook.

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