Completely invariant components of the Fatou sets of meromorphic maps are discussed. Positive answers are given to Baker’s and Bergweiler’s problems that such components are the only Fatou components for certain classes of meromorphic maps.
Both authors are supported by NSFC and the 973 Project.
"On completely invariant Fatou components." Ark. Mat. 41 (2) 253 - 265, October 2003. https://doi.org/10.1007/BF02390814