Abstract
We construct an analogue of Sierpiński gasket in Lobachevskii plane by means of iterated function system with maps from a transformation group of this space. The investigation of a new family of attractors and a Mandelbrot set associated with it reveals higher capacity of Lobachevskii geometry compared to that of Euclid.
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Submitted by M. M. Arslanov
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Troshin, P.I. On generalization of Sierpiński gasket in Lobachevskii plane. Lobachevskii J Math 38, 751–762 (2017). https://doi.org/10.1134/S1995080217040205
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DOI: https://doi.org/10.1134/S1995080217040205