The Golden mean, scale free extension of Real number system, fuzzy sets and $1/f$ spectrum in Physics and Biology

Details The Golden mean, scale free extension of Real number system, fuzzy sets and $1/f$ spectrum in Physics and Biology The Golden mean, scale free extension of Real number system, fuzzy sets and $1/f$ spectrum in Physics and Biology

2010-01-11

arxiv.org/abs/1001.1688v1

Chaos, Solitons and Fractals, vol 17, no. 4, 781-788, (2003)

Mathematics

General Mathematics

AMS_Latex 2e, 14 pages

Scientific paper

We show that the generic $1/f$ spectrum problem acquires a natural explanation in a class of scale free solutions to the ordinary differential equations. We prove the existence and uniqueness of this class of solutions and show how this leads to a nonstandard, fuzzy extension of the ordinary framework of calculus, and hence, that of the classical dynamics and quantum mechanics. The exceptional role of the golden mean irrational number is also explained.

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