Radial Distribution of Julia Sets of Entire Solutions to Complex Difference Equations

Abstract

In this paper, entire solutions f of a class of nonlinear difference equations are studied. By considering the order and deficiency of the coefficients in the equations, we investigate the properties of the radial distribution of the Julia set of f, and estimate the lower bound of the measure of the set defined by the common limiting directions of Julia sets of shifts of f.

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Correspondence to Yezhou Li.

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This work is supported by National Natural Science Foundation of China (Grant No. 11571049 and No. 11101048) and China Scholarship Council.

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Chen, J., Li, Y. & Wu, C. Radial Distribution of Julia Sets of Entire Solutions to Complex Difference Equations. Mediterr. J. Math. 17, 184 (2020). https://doi.org/10.1007/s00009-020-01627-y

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Keywords

  • Radial distribution
  • Julia set
  • nonlinear difference equation
  • deficiency

Mathematics Subject Classification

  • 30D35
  • 34M10
  • 37F10