A Family of Meromorphic Functions: Ergodic or Non-ergodic
Time: 2024-01-19
Published By: He Liu
Speaker(s): Tao Chen(City University of New York)
Time: 09:00-10:00 January 24, 2024
Venue: Online
McMullen's dichotomy states that a rational map is ergodic (the Julia set is the whole sphere, and the map is ergodic) or attracting (almost every point on the sphere is attracted to the post-critical set). However, it may be challenging to determine which case applied to a given map, of which the Julia set is the sphere. In this talk, for a family of meromorphic maps with finite many asymptotic values and no critical points, called Nevanlinna functions in the literature, we give a criterion to determine whether it is ergodic or not. This is a joint work with Yunping Jiang and Linda Keen.
Zoom Meeting ID: 181 155 584
