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Limit of Julia sets forz d +c

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Chinese Science Bulletin

Abstract

The limit behavior of Julia setJ(f d,c) for polynomialsf d,c(z) =z d +c is considered. That ¦J(f d,c)¦ d≥ 2 converges to the unit circle S1 in Hausdorff metric for some fixed parameterc is proved and some examples showing ¦ J(f d,c) ¦d>-2 has no limit are given.

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References

  1. Devaney, R. L., Goldbery, L. H., Hubbard, J., Dynamical approximation to the exponential map by polynomials,Technical Report MSRI. 1986. 10019–86.

  2. van Strien, S., Nowicki, T., Polynomial maps with a Julia yet of positive Lebesgue measure: Fibinacci maps,Stony Brook IMS, 1994, 3.

  3. Yin Yongcheng, Capacities and diameters of Julia sets of rational functions,M. S. Thesis. 1987.

  4. Tsuji, M.,Potential Theory in Modern Function Theory, Tokyo: Maruzen, 1959.

    Google Scholar 

  5. Bieberbach, L., Über einige Extremal probleme im Gebiete der konformen Abbildung,Math. Ann., 1916, 71: 153.

    Article  Google Scholar 

  6. Brolin, H., Invariant sets under iteration of rational functions,Arkiv, for Mat., 1965, B6: 103.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Zhejiang University, 310027, Hangzhou, China

    Yin Yongcheng

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  1. Yin Yongcheng
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Yin, Y. Limit of Julia sets forz d +c . Chin. Sci. Bull. 44, 595–598 (1999). https://doi.org/10.1007/BF03182715

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  • DOI: https://doi.org/10.1007/BF03182715

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