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The dynamics of semigroups of transcendental entire functions II

Author

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  • Dinesh Kumar

    (University of Delhi)

  • Sanjay Kumar

    (University of Delhi)

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.

Suggested Citation

  • Dinesh Kumar & Sanjay Kumar, 2016. "The dynamics of semigroups of transcendental entire functions II," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(3), pages 409-423, September.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:3:d:10.1007_s13226-016-0173-8
    DOI: 10.1007/s13226-016-0173-8
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    1. Dinesh Kumar & Sanjay Kumar, 2015. "The dynamics of semigroups of transcendental entire functions I," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(1), pages 11-24, February.
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    Cited by:

    1. Ramanpreet Kaur & Dinesh Kumar, 2021. "Results on escaping set of an entire function and its composition," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 79-86, March.

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    1. Ramanpreet Kaur & Dinesh Kumar, 2021. "Results on escaping set of an entire function and its composition," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 79-86, March.

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