论文标题
关于λ+ tan z^2的动力学
On Dynamics of λ+ tan z^2
论文作者
论文摘要
本文讨论了Meromorphic Maps $λ+λ+ \ tan z^2 $ for $λ\ in \ Mathbb c $的动态平面（$ z $ - 平面）的一些拓扑特性（$ z $ - 平面）。在动态平面中，我们证明没有赫尔曼环，当参数位于复杂平面中四个象限中包含的无界双曲线分量中时，朱莉娅集合是图形的cantor集。当参数位于参数平面的其他双曲分量中时，将朱莉娅集（Julia Set）连接为地图。
This article discusses some topological properties of the dynamical plane ($z$-plane) of the holomorphic family of meromorphic maps $λ+ \tan z^2$ for $ λ\in \mathbb C$. In the dynamical plane, we prove that there is no Herman ring, and the Julia set is a Cantor set for the maps when the parameter is in the unbounded hyperbolic component contained in the four quadrants in the complex plane. Julia set is connected for the maps when the parameters are in other hyperbolic components of the parameter plane.
