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) |
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Pages (from-to) | 99-115 |
Number of pages | 17 |
Journal | New York Journal of Mathematics |
Volume | 7 |
State | Published - 2001 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)