数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 143-155.doi: 10.1007/s10473-023-0109-4

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A NOTE ON THE JULIA SETS OF ENTIRE SOLUTIONS TO DELAY DIFFERENTIAL EQUATIONS*

Yezhou Li, Heqing Sun   

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
  • 收稿日期:2021-08-11 修回日期:2022-06-30 发布日期:2023-03-01
  • 通讯作者: †Heqing SUN.E-mail: heqingsuncg1@163.com
  • 基金资助:
    *National Natural Science Foundation of China (12171050, 12071047) and the Fundamental Research Funds for the Central Universities(500421126).

A NOTE ON THE JULIA SETS OF ENTIRE SOLUTIONS TO DELAY DIFFERENTIAL EQUATIONS*

Yezhou Li, Heqing Sun   

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
  • Received:2021-08-11 Revised:2022-06-30 Published:2023-03-01
  • Contact: †Heqing SUN.E-mail: heqingsuncg1@163.com
  • About author:Yezhou Li, E-mail: yezhouli@bupt.edu.cn
  • Supported by:
    *National Natural Science Foundation of China (12171050, 12071047) and the Fundamental Research Funds for the Central Universities(500421126).

摘要: Let $f$ be an entire solution of the Tumura-Clunie type non-linear delay differential equation. We mainly investigate the dynamical properties of Julia sets of $f$, and the lower bound estimates of the measure of related limiting directions is verified.

关键词: delay differential equation, dynamical properties, Julia sets, limiting directions

Abstract: Let $f$ be an entire solution of the Tumura-Clunie type non-linear delay differential equation. We mainly investigate the dynamical properties of Julia sets of $f$, and the lower bound estimates of the measure of related limiting directions is verified.

Key words: delay differential equation, dynamical properties, Julia sets, limiting directions