×

Disconnected Julia sets of quartic polynomials and a new topology of the symbol space. (English) Zbl 1154.37018

Summary: 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.

MSC:

37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37B10 Symbolic dynamics
37F99 Dynamical systems over complex numbers
PDFBibTeX XMLCite
Full Text: DOI Euclid

References:

[1] K. Katagata, On a certain kind of polynomials of degree 4 with disconnected Julia set, Discrete Contin. Dyn. Syst. 20 (2008), no. 4, 975-987. · Zbl 1151.37042 · doi:10.3934/dcds.2008.20.975
[2] J. L. Kelley, General topology , Reprint of the 1955 edition [Van Nostrand, Toronto, Ont.], Springer, New York, 1975.
[3] J. Milnor, Dynamics in one complex variable , Vieweg, Braunschweig, 1999. · Zbl 0946.30013
[4] S. Morosawa, Y. Nishimura, M. Taniguchi and T. Ueda, Holomorphic dynamics , Translated from the 1995 Japanese original and revised by the authors, Cambridge Univ. Press, Cambridge, 2000. · Zbl 0979.37001
[5] J. Nagata, Modern general topology , Second revised edition, North-Holland, Amsterdam, 1974.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.