On Dynamics of λ+ tan z^2
Year: 2022
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Nandi, Santanu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4303424403