A new family of entire functions with no wandering domains
11 Oct 2019
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Dourekas Yannis
The issue of whether an analytic function has wandering domains has long been
of interest in complex dynamics. Sullivan proved in 1985 that rational maps do
not have wandering domains...On the other hand, several transcendental entire
functions have wandering domains. Using recent results on the relationship
between Fatou components and the postsingular set, we find a new family of
transcendental entire functions that does not have wandering domains. We also
prove that the Julia set of a certain subfamily is the whole plane.(read more)