Journal d'Analyse Mathématique

, 102:119

Infinitesimal generators associated with semigroups of linear fractional maps

  • Filippo Bracci
  • Manuel D. Contreras
  • Santiago Díaz-Madrigal
Article

DOI: 10.1007/s11854-007-0018-9

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

Abstract

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.

Copyright information

© The Hebrew University of Jerusalem 2007

Authors and Affiliations

  • Filippo Bracci
    • 1
  • Manuel D. Contreras
    • 2
  • Santiago Díaz-Madrigal
    • 2
  1. 1.Dipartimento Di MatematicaUniversità Di Roma “tor Vergata”RomaItaly
  2. 2.Camino De Los Descubrimientos, S/N Departamento De Matemática Aplicada II Escuela Superior De IngenierosUniversidad De SevillaSevillaSpain