Infinitesimal generators associated with semigroups of linear fractional maps
- Cite this article as:
- Bracci, F., Contreras, M.D. & Díaz-Madrigal, S. J Anal Math (2007) 102: 119. doi:10.1007/s11854-007-0018-9
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We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in ℂn, n ≥ 1. For the case n = 1, we also completely describe the associated Koenigs function and 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.