Results on escaping set of an entire function and its composition

Ramanpreet Kaur; Dinesh Kumar

Results on escaping set of an entire function and its composition

Dynamical Systems 2019-03-20 v3

Authors: Ramanpreet Kaur , Dinesh Kumar

Abstract

Given two permutable entire functions $f$ and $g,$ we establish vital relationship between escaping sets of entire functions $f, g$ and their composition. We provide some families of transcendental entire functions for which Eremenko's conjecture holds. In addition, we investigate the dynamical properties of the mapping $f(z)=z+1+e^{-z}.$

Keywords

escaping set entire function transcendental entire function Eremenko's conjecture complex dynamics composition

Cite

@article{arxiv.1609.03915,
  title  = {Results on escaping set of an entire function and its composition},
  author = {Ramanpreet Kaur and Dinesh Kumar},
  journal= {arXiv preprint arXiv:1609.03915},
  year   = {2019}
}

Comments

Work in progress. Comments are welcome. arXiv admin note: text overlap with arXiv:1401.0425, arXiv:1406.2453

Results on escaping set of an entire function and its composition

Abstract

Keywords

Cite

Comments

Related papers