Wandering on the boundary

Abstract: In the theory of iteration of transcendental entire functions, wandering domains, i.e. connected components of the Fatou set that are not eventually periodic, have been extensively studied in recent years. For example, a nine-way classification of the internal dynamics in simply connected wandering domains has been given. In this talk we focus on the dynamical behaviour on the boundaries of simply connected wandering domains. In particular, we consider the possibility that most boundary orbits converge together in a certain sense, and give sufficient conditions for such a convergence to hold. Our results are motivated by and extend classical results on the boundary dynamics of inner functions.

This is work in progress joint with A.M. Benini, N. Fagella, P. Rippon and G. Stallard.

complex variablesdynamical systems

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

Series comments: Please e-mail R.Halburd@ucl.ac.uk for the Zoom link. Also, please let me know whether you would like to be added to the mailing list to automatically receive links for future talks in CAvid.