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

Boris Solomyak

doi:10.1007/BF02901438

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

Boris Solomyak

University of Washington

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	149-157
Number of pages	9
Journal	Analysis in Theory and Applications
Volume	20
Issue number	2
DOIs	https://doi.org/10.1007/BF02901438
State	Published - Jun 2004
Externally published	Yes

Bibliographical note

Funding Information:
Supporte in part by NSF grant #DMS 0099814.

Funding

Supporte in part by NSF grant #DMS 0099814.

Funders	Funder number
National Science Foundation	0099814

Keywords

Iterated function system
Local geometry
Mandelbrot set

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10.1007/BF02901438

Cite this

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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.",

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AB - 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.

KW - Iterated function system

KW - Local geometry

KW - Mandelbrot set

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

Abstract

Bibliographical note

Funding

Keywords

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