Escaping set and Julia set of transcendental semigroups

Dinesh KUMAR, Sanjay KUMAR, Kin Keung Eric POON

Research output: Contribution to journalArticle

Abstract

We discuss the dynamics of semigroups of transcendental entire functions using Fatou-Julia theory and provide a condition for the complete invariance of escaping set and Julia set of transcendental semigroups. Results regarding limit functions and postsingular set are also derived. In addition, classes of hyperbolic and postsingularly bounded transcendental semigroups are given. We also provide certain criterion for non existence of wandering domains of transcendental semigroups. Copyright © 2016 Research India Publications.
Original languageEnglish
Pages (from-to)423-436
JournalAdvances in Theoretical and Applied Mathematics
Volume11
Issue number4
Publication statusPublished - 2016

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Julia set
Transcendental
Semigroup
Transcendental function
Entire Function
Nonexistence
Invariance

Citation

Kumar, D., Kumar, S., & Poon, K. K. (2016). Escaping set and Julia set of transcendental semigroups. Advances in Theoretical and Applied Mathematics, 11(4), 423-436.

Keywords

  • Semigroup
  • Normal family
  • Completely invariant
  • Hyperbolic