On the connectivity of the Julia set of meromorphic maps. The case of (rational or transcendental) meromorphic Newton maps [ Back ]

15:30 to 16:30
UAB - Dept. Matemàtiques (C1/-128)
Xavier Jarque


After Shishikura's paper (1990) on the connectivity of Julia sets for rational maps (in terms of the weakly repelling fixed points), different authors had considered the case of transcendental meromorphic maps. The final statement in the transcendental scenario is the following: If the Julia set of a transcendental meromorphic map $f$ is disconnected (in other words, the Fatou set has a multiply connected component) then $f$ has, at least, one (weakly) repelling fixed point.

In particular the Julia set of transcendental meromorphic Newton maps is connected.

The proof of the main result follows from the results of 4 papers and different techniques. We will show that when we restrict to (rational or transcendental) meromorphic Newton maps, the proof is much simpler and can be somehow unified.

This is a joint work with K. Baranski, N. Fagella, and B. Karpinska.