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Multivalued fractals and hyperfractals

机译:多值分形和超分形

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摘要

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 & Fier, 2004; Andres et al., 2005]. In the case of uniqueness, they also coincide with the supports of invariant measures of the associated MarkovFeller 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.
机译:系统地研究了一类称为超分形的新分形。它们在支撑空间中的基本分形是我们自己在较早的论文中开发的多值分形[Andres&Fier,2004; Andres等,2005]。在唯一性的情况下,它们还与相关的MarkovFeller超算子的不变度量的支持一致。我们通过超空间中的不动点定理证明它们的存在,并在生成超图的特定情况下计算其Hausdorff维数。提供了两个说明性示例。

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