The dynamics of semigroups of transcendental entire functions I

Abstract

We consider the dynamics associated with an arbitrary semigroup of transcendental entire functions. Fatou-Julia theory is used to investigate the dynamics of these semigroups. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroup case. We also investigate the dynamics of conjugate semigroups, abelian transcendental semigroups and wandering and Baker domains of transcendental semigroups.2010 Mathematics Subject Classification. 37F10, 30D05.

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