2 .家庭动态

Far East Journal of Dynamical Systems Pub Date : 2020-05-30 DOI:10.17654/DS032020067

Santanu Nandi

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引用次数: 2

摘要

本文讨论了$ \lambda \in \mathbb C^*$的亚纯映射$\lambda \tan z^2$的全纯族的动力平面($z$ -平面)的一些拓扑性质。在动力平面上，证明了当参数在包含原点的双曲分量内时，映射的Julia集是Cantor集，且不存在Herman环。当参数在参数平面的其他双曲组件中时，Julia集连接映射。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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DYNAMICS OF THE FAMILY tan z2

This article discusses some topological properties of the dynamical plane ($z$-plane) of the holomorphic family of meromorphic maps $\lambda \tan z^2$ for $ \lambda \in \mathbb C^*$. In the dynamical plane, I prove that there is no Herman ring and the Julia set is a Cantor set for the maps when the parameter is in the hyperbolic component containing the origin. Julia set is connected for the maps when the parameters are in other hyperbolic components in the parameter plane.

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Far East Journal of Dynamical Systems

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