On Hausdorff dimension of random fractals

A. V. Dryakhlov, A. A. Tempelman

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Abstract

We study random recursive constructions with finite "memory" in complete metric spaces and the Hausdorff dimension of the generated random fractals. With each such construction and any positive number β we associate a linear operator V(β) in a finite dimensional space. We prove that under some conditions on the random construction the Hausdorff dimension of the fractal coincides with the value of the parameter β for which the spectral radius of V(β) equals 1.

Original languageEnglish (US)
Pages (from-to)99-115
Number of pages17
JournalNew York Journal of Mathematics
Volume7
Publication statusPublished - Dec 1 2001

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Dryakhlov, A. V., & Tempelman, A. A. (2001). On Hausdorff dimension of random fractals. New York Journal of Mathematics, 7, 99-115.