Entire functions of slow growth whose Julia set contains any infinite collection of quasiconformal copies of polynomial Julia sets

Abstract

We prove that for any infinite collection of polynomial Julia sets of arbitrary degree at least two, there exists a transcendental entire function of arbitrarily slow growth such that its Julia set contains quasiconformal copies of the given polynomial Julia sets.

Keywords:

• Julia sets
• polynomial-like maps
• quasiconformal/quasiregular maps

2010 Mathematics Subject Classifications:

• Primary 37F10
• Secondary 30D05
• 37F50

Acknowledgements

I would like to thank the referees for their valuable comments and suggestions that have improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Grant-in-Aid for Young Scientists (B) No. 17K14212 of the Japan Society for the Promotion of Science.