## Finitely generated subgroups of , I. Formal theory.

- Formal normal form for a single holomorphic self-map from . Parabolic germs.
- Bochner theorem on holomorphic linearization of finite groups.
- Stratification of the subgroup of parabolic germs .
- Tits alternative for finitely generated subgroups of :
*every such subgroup is either metabelian (its commutator is commutative, e.g., trivial), or non-solvable (all iterated commutators are nontrivial).* - Centralizers and symmetries: formal classification of solvable subgroups.
- Integrable germs and their holomorphic linearizability.

Recommended reading: Section 6 (first part) from the book (printing disabled)

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