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MULTIVALUED FRACTALS AND HYPERFRACTALS

Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. Listopadu 12, 77146 Olomouc, Czech Republic

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MIPOSLAV RYPKA

Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. Listopadu 12, 77146 Olomouc, Czech Republic

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https://doi.org/10.1142/S0218127412500095Cited by:23 (Source: Crossref)

Abstract

A new class of fractals called hyperfractals is systematically investigated. Their underlying fractals in supporting spaces are multivalued fractals developed by ourselves in our earlier papers [Andres & Fiser, 2004; Andres et al., 2005]. In the case of uniqueness, they also coincide with the supports of invariant measures of the associated Markov–Feller hyperoperators. We prove their existence by means of fixed point theorems in hyperspaces and calculate, in particular cases of generating hypermaps, their Hausdorff dimension. Two illustrative examples are supplied.

Supported by the Council of the Czech Government (MSM 6198959214).

Keywords:

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