, Volume 20, Issue 2, pp 149-157

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

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Abstract

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.

This paper was presented in the fractal Satellite Conference of ICM 2002 in Nanjing.
Supporte in part by NSF grant #DMS 0099814.