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Infinitesimal generators associated with semigroups of linear fractional maps

Filippo Bracci·Manuel D. Contreras·Santiago Diaz-Madrigal
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Abstract

We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in $\mathbb C^n$, $n\geq 1$. 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.

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Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal. 2006-01-27. Infinitesimal generators associated with semigroups of linear fractional maps. https://arxiv.org/abs/math/0601665

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