Permutable entire functions and multiply connected wandering domains

Benini, Anna Miriam; Rippon, Philip J. and Stallard, Gwyneth M. (2016). Permutable entire functions and multiply connected wandering domains. Advances in Mathematics, 287 pp. 451–462.

DOI: https://doi.org/10.1016/j.aim.2015.04.031

Abstract

Let f and g be permutable transcendental entire functions. We use a recent analysis of the dynamical behaviour in multiply connected wandering domains to make progress on the long standing conjecture that the Julia sets of f and g are equal; in particular, we show that J(f)=J(g) provided that neither f nor g has a simply connected wandering domain in the fast escaping set.

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