Noise and chaotic disturbance on self-similar sets

zbMATH Open0940.28010arXivmath/9812144MaRDI QIDQ1300195

Zu-Guo Yu, Fuyao Ren

Publication date: 19 July 2000

Published in: Southeast Asian Bulletin of Mathematics (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/math/9812144

zbMATH Keywords

collapsechaotic maptent mapchaotic disturbancenoise on self-similiar sets

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Fractals (28A80) Iteration of real functions in one variable (26A18)

Related Items (2)

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