2022/04/01 by Nandi, Santanu
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2204.00365
This article discusses some topological properties of the dynamical plane (z-plane) of the holomorphic family of meromorphic maps λ+ tan z2 for λ∈ \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.