On the dynamics of lambda*tan(z).

Title: On the dynamics of lambda*tan(z).
Identifier: AAI9119640
identifier: 9119640
Creator: Jiang, Weihua.
Contributor: Adviser: Linda Keen
Date: 1991
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: We study the dynamics of the family {dollar}T\sb\lambda{dollar}: {dollar}z \to \lambda{dollar} tan z of a single complex parameter. We describe the stable and chaotic behavior in the dynamical plane with a classification of the attracting cycles of {dollar}T\sb\lambda{dollar} and their multipliers. We show that the parameter plane contains infinitely many components which are appeared in pairs except the punctured unit disk. For {dollar}\lambda{dollar} in each component {dollar}\Omega{dollar}, {dollar}\{lcub}T\sb\lambda\{rcub}{dollar} is a quasi-conformal family. We use the internal arguments of the internal rays of {dollar}\Omega{dollar} to study the bifurcation on the boundary of {dollar}\Omega{dollar}. For any component {dollar}\Omega{dollar}, bud components are attached to it at all boundary points with rational internal argument. The periods, the size, and the location of these components, and the "virtual centers" of the component pairs and their coding are discussed in this thesis.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.