### 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 language | English (US) |
---|---|

Pages (from-to) | 99-115 |

Number of pages | 17 |

Journal | New York Journal of Mathematics |

Volume | 7 |

State | Published - 2001 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*New York Journal of Mathematics*,

*7*, 99-115.

}

*New York Journal of Mathematics*, vol. 7, pp. 99-115.

**On Hausdorff dimension of random fractals.** / Dryakhlov, A. V.; Tempelman, Arkady.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On Hausdorff dimension of random fractals

AU - Dryakhlov, A. V.

AU - Tempelman, Arkady

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=3042552229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042552229&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:3042552229

VL - 7

SP - 99

EP - 115

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

ER -