** Clifford Gilmore ** Université Clermont Auvergne

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Universality of composition operators and applications to complex dynamics
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Abstract:

We consider universality properties of composition operators C_{f} : g
↦ g ○ f, acting on spaces of holomorphic functions, where the symbol
f is given by a transcendental entire function restricted to parts of its Fatou
set F(f). The investigation of this topic was initiated by Jung [J. Anal. Math.,
2019], and it lies at the interface of complex dynamics and operator theory.

We will discuss new results on the universality of C_{f} when the symbol f is
restricted to certain Baker and wandering domains. In the case where such
universal functions exist, we will describe their local behaviour near points of
f that have specific dynamical properties. We will also consider the more
general class of weighted composition operators in this context, where we
uncover analogous universality results for this larger class.

(This is joint work with Vasiliki Evdoridou and Myrto Manolaki).