Quartic Julia sets including any two copies of  quadratic Julia sets

Koh  Katagata

doi:10.3934/dcds.2016.36.2103

Article Contents

2016, Volume 36, Issue 4: 2103-2112. Doi: 10.3934/dcds.2016.36.2103

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Quartic Julia sets including any two copies of quadratic Julia sets

Koh Katagata^1,

1.
National Institute of Technology, Ichinoseki College, Takanashi, Hagisho, Ichinoseki, Iwate 021-8511

Received: December 31, 2014

Revised: June 30, 2015

Published: May 2017

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Abstract

If the Julia set of a quartic polynomial with certain conditions is neither connected nor totally disconnected, there exists a homeomorphism between the set of all components of the filled-in Julia set and some subset of the corresponding symbol space. The question is to determine the quartic polynomials exhibiting such a dynamics and describe the topology of the connected components of their filled-in Julia sets. In this paper, we answer the question, namely we show that for any two quadratic Julia sets, there exists a quartic polynomial whose Julia set includes copies of the two quadratic Julia sets.

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Mathematics Subject Classification: Primary: 37F10; Secondary: 30D05, 37F50.

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References

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