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 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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On Hausdorff dimension of random fractals. / Dryakhlov, A. V.; Tempelman, Arkady.
In: New York Journal of Mathematics, Vol. 7, 2001, p. 99-115.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 -