Analysis in Theory and Applications

, Volume 20, Issue 2, pp 149-157

First online:

“Mandelbrot set” for a pair of linear maps: The local geometry

  • Boris SolomyakAffiliated withDepartment of Mathematics, University of Washington Email author 

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We consider the iterated function system {λz−1, λz+1} in the complex plane, for λ 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.

Key words

Mandelbrot set iterated function system local geometry

AMS(2000)subject classification

28A80 28A78 37F45 26C10