Derived length of solvable groups of local diffeomorphisms

Abstract

Let $G$ be a solvable subgroup of the group $\diff{}{n}$ of local complex analytic diffeomorphisms. Analogously as for groups of matrices we bound the solvable length of $G$ by a function of $n$. Moreover we provide the best possible bounds for connected, unipotent and nilpotent groups.

arXiv comment27 pages

References in corpus (1)

• Embedding smooth and formal diffeomorphisms through the Jordan-Chevalley decomposition

Cited by in corpus (6)

• Finite dimensional groups of local diffeomorphisms
• The solvable length of groups of local diffeomorphisms
• Recurrent orbits of subgroups of local complex analytic diffeomorphisms
• Stable manifolds of biholomorphisms in ${\mathbb{C}}^n$ asymptotic to formal curves
• Boundness of intersection numbers for actions by two-dimensional biholomorphisms
• Integrating factors for groups of formal complex diffeomorphisms