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The dynamics of semigroups of transcendental entire functions II

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Delhi, 110 007, India

    Dinesh Kumar

  2. Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi, New Delhi, 110 015, India

    Sanjay Kumar

Authors
  1. Dinesh Kumar
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  2. Sanjay Kumar
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Corresponding author

Correspondence to Dinesh Kumar.

Additional information

The research work of the first author is supported by research fellowship from Council of Scientific and Industrial Research (CSIR), New Delhi.

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Kumar, D., Kumar, S. The dynamics of semigroups of transcendental entire functions II. Indian J Pure Appl Math 47, 409–423 (2016). https://doi.org/10.1007/s13226-016-0173-8

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  • DOI: https://doi.org/10.1007/s13226-016-0173-8

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