“Auxiliary Lesson” שעור עזר) #8) December 13, 2007

Wednesday, December 12, 2007

Formal normal form for a single holomorphic self-map from $\text{Diff}(\mathbb C^1,0)$ . Parabolic germs.
Bochner theorem on holomorphic linearization of finite groups.
Stratification of the subgroup of parabolic germs $\text{Diff}_1(\mathbb C^1,0)$ .
Tits alternative for finitely generated subgroups of $\text{Diff}(\mathbb C^1,0)$ : 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.

Disclaimer applies, as usual

Comments (1)

The formula (6.10) on page 88 contains a typo: the right formula should be $G_{p,0}'=\{b\cdot \exp t F_{p,0}\colon b\in\mathbb C^*,\ t\in\mathbb C\}$ .

This comment is at the same time an invitation to submit corrections of typos and more grave errors in the textbook. The list will be maintained by AMS and serve the community of future readers.

Comment by Sergei Yakovenko — Saturday, December 15, 2007 @ 8:32 | Reply