Search arXiv⌕ Search

arXiv subjects

Fu-Yao Ren

Publications and source records attributed to Fu-Yao Ren.

2 recordsLinked to original sources
arXiv1998

Noise and chaotic disturbance on self-similar set

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.

math.CA↗
arXiv1998

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 which is the invariant compact set of infinite contractive similarities {S_j(x)} satisfying open set condition is obtained. It is proved (under some additional hypotheses) that the mean quadratic variation of infinite self-similar measure is of asymptotic property.

math.CA↗