Infinitesimal generators associated with semigroups of linear fractional maps

Abstract

We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in ${\mathbb{C}}^n$, $n\ge 1$. For the case $n=1$ we also completely describe the associated Koenigs function and we solve the embedding problem from a dynamical point of view, proving, among other things, that a generic semigroup of holomorphic self-maps of the unit disc is a semigroup of linear fractional maps if and only if it contains a linear fractional map for some positive time.

21 pages

References in corpus (1)

• On Valiron's Theorem