Infinitesimal generators associated with semigroups of linear fractional maps

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. Partially supported by the Ministerio de Ciencia y Tecnología and the European Union (FEDER) project BFM2003-07294-C02-02 and by La Consejería de Educación y Ciencia de la Junta de Andalucía.