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Full-Text Articles in Physical Sciences and Mathematics
Dynamics Of The Family Lambda Tan Z^2, Santanu Nandi
Dynamics Of The Family Lambda Tan Z^2, Santanu Nandi
Dissertations, Theses, and Capstone Projects
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 …
On The Dynamics Of Quasi-Self-Matings Of Generalized Starlike Complex Quadratics And The Structure Of The Mated Julia Sets, Ross Flek
Dissertations, Theses, and Capstone Projects
It has been shown that, in many cases, Julia sets of complex polynomials can be "glued" together to obtain a new Julia set homeomorphic to a Julia set of a rational map; the dynamics of the two polynomials are reflected in the dynamics of the mated rational map. Here, I investigate the Julia sets of self-matings of generalized starlike quadratic polynomials, which enjoy relatively simple combinatorics. The points in the Julia sets of the mated rational maps are completely classified according to their topology. The presence and location of buried points in these Julia sets are addressed. The interconnections between …