"MANDELBROT SET" FOR A PAIR OF LINEAR MAPS: THE LOCAL GEOMETRY

作     者：Boris Solomyak 

作者机构：University of Washington USAe consider the iterated function system {λz-1 λz + 1} in the complex plane for A in the open unit disk. Let M be the set of λsuch that the attractor of the IFS is connected. We discuss some topological and geometric properties of the set M and prove a new result about possible corners on its boundary. Some open problems and directions for further research are discussed as well. 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2004年第20卷第2期

页      面：149-157页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：in part by NSF grant #DMS 0099814 

主　　题：Mandelbrot set iterated function system local geometry 

摘      要：We consider the iterated function system {λz-1, λz + 1} in the complex plane, for A in the open unit disk. Let M be the set of λ such that the attractor of the IFS is connected. We discuss some topological and geometric properties of the set M and prove a new result about possible corners on its boundary. Some open problems and directions for further research are discussed as well.