Absorbing domains, connectivity of the Julia set and weakly repelling fixed points [ Back ]

Date:
20.04.12   
Times:
09:30 to 10:30
Place:
IMUB - Universitat de Barcelona
Speaker:
Nuria Fagella and Xavier Jarque
University:
Universitat de Barcelona

Abstract:

We will discuss the existence of absorbing domains for meromorphic transcendental functions and we will show how to use them to prove the following result: Let $f$ be a meromorphic map. If the Julia set is not connected then $f$ must have at least one weakly repelling fixed point. This result is the transcendental version of a Theorem due to Shishikura for rational maps: Let $f$ be a rational map of degree at least two. If the Julia set is not connected then $f$ must have at least two weakly repelling fixed point. The results we will discuss are part of a joint work with K. Baranski and B. Karpinska.