Classifying internal dynamics in simply connected wandering domains [ Back ]

Date:
11.03.19   
Times:
15:00 to 16:00
Place:
Aula T1
Speaker:
Núria Fagella
University:
Universitat de Barcelona

Abstract

We study the internal dynamics of simply connected, bounded wandering domains of a transcendental entire map f. While the dynamics on periodic Fatou components and on multiply connected wandering domains are well understood, the internal dynamics on simply connected, bounded wandering domains have so far eluded classi cation. We fi ll this gap by classifying dynamics on simply connected wandering domains in terms of the hyperbolic distance between iterates and, at the same time, by whether orbits converge to the boundary of the sequence of domains. These classi cations de ne nine possible cases which we show, using approximation theory, that they are realizable. We deduce a general technique for constructing examples of this type.