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Quartic Julia sets including any two copies of quadratic Julia sets

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

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  • [1]

    P. Blanchard, Disconnected Julia sets, chaotic dynamics and fractals, Notes Rep. Math. Sci. Engrg., Academic Press, Orlando, FL, 2 (1986), 181-201.

    [2]

    A. Douady and J. Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. Éc. Norm. Sup. (4), 18 (1985), 287-343.

    [3]

    K. Katagata, On a certain kind of polynomials of degree 4 with disconnected Julia set, Discrete Contin. Dyn. Syst. , 20 (2008), 975-987.doi: 10.3934/dcds.2008.20.975.

    [4]

    M. Kisaka and M. Shishikura, On multiply connected wandering domains of entire functions, Transcendental dynamics and complex analysis, London Math. Soc. Lecture Note Ser. Cambridge Univ. Press, Cambridge, 348 (2008), 217-250.doi: 10.1017/CBO9780511735233.012.

    [5]

    S. Morosawa, Y. Nishimura, M. Taniguchi and T. Ueda, Holomorphic Dynamics, Cambridge Studies in Advanced Mathematics, 66. Cambridge University Press, Cambridge, 2000.

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