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July 2008 Disconnected Julia sets of quartic polynomials and a new topology of the symbol space
Koh Katagata
Proc. Japan Acad. Ser. A Math. Sci. 84(7): 117-122 (July 2008). DOI: 10.3792/pjaa.84.117

Abstract

For a certain quartic polynomial, there exists a homeomorphism between the set of all components of the filled-in Julia set with the Hausdorff metric and some subset of the corresponding symbol space with the ordinary metric. But these sets are not compact with respect to each metric. We introduce a new topology with respect to which these sets are compact.

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Koh Katagata. "Disconnected Julia sets of quartic polynomials and a new topology of the symbol space." Proc. Japan Acad. Ser. A Math. Sci. 84 (7) 117 - 122, July 2008. https://doi.org/10.3792/pjaa.84.117

Information

Published: July 2008
First available in Project Euclid: 17 July 2008

zbMATH: 1154.37018
MathSciNet: MR2450063
Digital Object Identifier: 10.3792/pjaa.84.117

Subjects:
Primary: 37F10
Secondary: 37B10

Keywords: disconnected Julia sets , Quartic polynomials , symbolic dynamics

Rights: Copyright © 2008 The Japan Academy

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Vol.84 • No. 7 • July 2008
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