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"MANDELBROT SET" FOR A PAIR OF LINEAR MAPS:THE LOCAL GEOMETRY |
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| Authors: | Boris Solomyak |
| 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. |
| Keywords: | Mandelbrot set iterated function system local geometry MANDELBROT MAPS LINEAR PAIR problems research geometric properties prove result boundary attractor open unit disk complex plane iterated function system |
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