The dynamics of semigroups of transcendental entire functions II

Dinesh Kumar () and Sanjay Kumar ()
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Dinesh Kumar: University of Delhi
Sanjay Kumar: University of Delhi

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 3, 409-423

Abstract: Abstract We introduce the concept of escaping set for semigroups of transcendental entire functions using Fatou-Julia theory. Several results of the escaping set associated with the iteration of one transcendental entire function have been extended to transcendental semigroups. We also investigate the properties of escaping sets for conjugate semigroups and abelian transcendental semigroups. Several classes of transcendental semigroups for which Eremenko’s conjecture holds have been provided.

Keywords: Escaping set; normal family; postsingular set; bounded type; hyperbolic (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0173-8

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