We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in C-n, 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.
Bracci, F., Contreras, M.d., Diaz Madrigal, S. (2007). Infinitesimal generators associated with semigroups of linear fractional maps. JOURNAL D'ANALYSE MATHEMATIQUE, 102, 119-142 [10.1007/s11854-007-0018-9].
Infinitesimal generators associated with semigroups of linear fractional maps
BRACCI, FILIPPO;
2007-01-01
Abstract
We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in C-n, 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.