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)|
|Number of pages||17|
|Journal||New York Journal of Mathematics|
|Publication status||Published - Dec 1 2001|
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