Catastrophes in the multi-fractal dynamics of social-economic systems |
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| Authors: | A. N. Kudinov V. P. Tsvetkov I. V. Tsvetkov |
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| Affiliation: | (1) Department of Geology, Ball State University, Muncie, Indiana, 47306;(2) Department of Mathematical Sciences, Ball State University, Muncie, Indiana, 47306 |
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| Abstract: | In the present paper, the concept of multi-fractal dynamics is developed. The problem concerning catastrophes in this dynamics is studied in detail. In the framework of the concept of fractal curve as a thick curve, it is proved that the cell approach to measuring the fractal dimension D is equivalent to measuring the dependence of the length L of the line on the scope δ. The introduction of a fractal scale of temperatures T f is suggested. |
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