Compositionally universal entire functions on the plane and the punctured plane

Description

Necessary/sufficient conditions for a sequence of automorphisms of the complex plane to generate a sequence of composition operators that is universal on the punctured plane are provided. As a consequence, it is derived that only for translations and rotation-dilations there can be entire functions whose orbits present universality. Boundedness of these functions on unbounded sets as well as frequent universality on the whole plane are also analyzed.

Abstract

Plan Andaluz de Investigación (Junta de Andalucía)

Abstract

Ministerio de Ciencia e Innovación

Abstract

Ministerio de Ciencia y Tecnología (MCYT). España

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