Pierre MOUSSA

Service de Physique Theorique, 
C. E. A- Saclay F-91191 Gif Sur Yvette Cedex
France
moussa@spht.saclay.cea.fr

Real and complex Brjuno functions (work in collaboration with S. Marmi (Florence), and J.-C. Yoccoz, (College de France, Paris)

Abstract: We discuss the properties of the Brjuno functions, introduced by Yoccoz to describe the size of the stability domains in discrete holomorphical dynamical systems close to a rotation. We analyse in particular the complex extension of these functions, and try to characterize their singularity on the real axis. This is a non trivial model where one can describe in a global way the singularities generated by small divisors problems