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The rational maps F λ (z) = z m + λ/z d have no Herman rings

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Abstract

It is proved that the rational maps in the family {z → z m+λ/z d: λ ∈ ℂ\{0}} for integers m, d ≥ 2 have no Herman rings.

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Authors and Affiliations

  1. College of Mathematics and Economics, Hunan University, Changsha, 410082, China

    Yingqing Xiao

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Weiyuan Qiu

Authors
  1. Yingqing Xiao
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  2. Weiyuan Qiu
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Correspondence to Yingqing Xiao.

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Xiao, Y., Qiu, W. The rational maps F λ (z) = z m + λ/z d have no Herman rings. Proc Math Sci 120, 403–407 (2010). https://doi.org/10.1007/s12044-010-0044-x

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  • DOI: https://doi.org/10.1007/s12044-010-0044-x

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