Chun-Lei CaoInstitute of Mathematics Academy of Mathematics and System Sciences, Chinese Academy of SciencesYue-Fei WangInstitute of Mathematics Academy of Mathematics and System Sciences, Chinese Academy of Sciences
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.
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It is known that finitely generated FI-modules over a field of characteristic 0 are Noetherian. We generalize this result to the abstract setting of an infinite EI category satisfying certain combinatorial conditions.