2 5 D ec 1 99 8 Noise and chaotic disturbance on self - similar set ∗
نویسندگان
چکیده
The effect of noise on self-similar set is studied. The iteratie procedure used to generate the self-similar set is moidified by adding a stochastic variable to the diameter of generating sets at each iteration. The noise may causes the generating set to collapse to a point. Distribution functions are found describing the probability that any generating set collapse. The effect of chaotic disturbance on the iteration of self-similar set is studied. It is shown that the iterative procedure which describes the self-similar set is truncated under the influence of disturbance generated by the tent map. Conditions which lead to truncation of any chaotic map are also obtained.
منابع مشابه
2 4 D ec 1 99 8 Hausdorff dimension , Mean quadratic variation of infinite self - similar measures ∗
Under weaker condition than that of Riedi & Mandelbrot, the Hausdorff (and Hausdorff-Besicovitch) dimension of infinite self-similar set K ⊂ R which is the invariant compact set of infinite contractive similarities {Sj(x) = ρjRjx + bj}j∈N (0 < ρj < 1, bj ∈ R , Rj orthogonal) satisfying open set condition is obtained. It is proved (under some additional hypotheses) that the β-mean quadratic vari...
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