Analysis in Theory and Applications

, Volume 20, Issue 2, pp 149–157

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


DOI: 10.1007/BF02901438

Cite this article as:
Solomyak, B. Anal. Theory Appl. (2004) 20: 149. doi:10.1007/BF02901438


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 

Copyright information

© Springer 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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