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

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Analysis in Theory and Applications

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, 98195-4350, Seattle, WA, USA

    Boris Solomyak

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  1. Boris Solomyak
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Correspondence to Boris Solomyak.

Additional information

This paper was presented in the fractal Satellite Conference of ICM 2002 in Nanjing.

Supporte in part by NSF grant #DMS 0099814.

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Solomyak, B. “Mandelbrot set” for a pair of linear maps: The local geometry. Anal. Theory Appl. 20, 149–157 (2004). https://doi.org/10.1007/BF02901438

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  • DOI: https://doi.org/10.1007/BF02901438

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