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Capacities of Julia sets of rational functions

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Abstract

For any polynomialp(z)=a 0 z n+a|z n−1+⋯+a n , a0≠0, n⩾2,F is the Julia set andμ * is the equilibrium distribution onF. Hans Brolin[1] proved thatγ (F)>0, andS *μ =F. Up to now, we know nothing about rational functions. The aim of this paper is to discuss the case of rational functions.

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References

  1. Hans Brolin, Invariant sets under iteration of rational functions,Arkiv for Matematik,6 (1965), 103–144.

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  2. Tsuji, M., Potential theory in modern function theory, Maruzen, Tokyo, 1959.

  3. Paul Blanchard, Complex analytic dynamics on the Riemann sphere,Bull. Amer. Math. Soc.,11 (1984), 85–141.

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  4. Oba M. K. and T. S. Pitcher, A new characterization of theF set of a rational function,Trans. Amer. Math. Soc.,166 (1972), 297–308.

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Authors and Affiliations

  1. Institute of Mathematics, Fudan University, China

    Yin Yongcheng

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  1. Yin Yongcheng
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Project supported by the Science Fund of the Chinese Academy of Sciences.

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Yongcheng, Y. Capacities of Julia sets of rational functions. Acta Mathematica Sinica 6, 120–130 (1990). https://doi.org/10.1007/BF02107591

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  • DOI: https://doi.org/10.1007/BF02107591

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