Dissertations, Theses, and Capstone Projects
Date of Degree
9-2019
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Linda Keen
Committee Members
Yunping Jiang
Sudeb Mitra
Frederick Gardiner
Subject Categories
Dynamical Systems | Mathematics | Physical Sciences and Mathematics
Keywords
complex dynamics, quasiconformal surgery, Cantor set, dynamics of meromorphic maps
Abstract
We prove some topological properties of the dynamical plane ($z$-plane) and a combinatorial structure of the parameter plane of a holomorphic family of meromorphic maps $\lambda \tan z^2$. In the dynamical plane, we prove that there is no Herman ring and the Julia set is a Cantor set for the map when the parameter is in the central capture component. Julia set is connected for the maps when the parameters are in other hyperbolic components. In the parameter plane, I prove that the capture components are simply connected and there are always four hyperbolic shell components attached to a virtual center. The capture components and the periodic shell components of the period greater than one are bounded.
Recommended Citation
Nandi, Santanu, "Dynamics of the Family lambda tan z^2" (2019). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/3297