The golden mean, scale free extension of real number system, fuzzy sets and \(1/f\) spectrum in physics and biology. (English) Zbl 1032.26502

Datta, Dhurjati Prasad

Chaos Solitons Fractals 17, No. 4, 781-788 (2003).

Summary: 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.

MSC:

26E50	Fuzzy real analysis
00A79	Physics
26E35	Nonstandard analysis
34A99	General theory for ordinary differential equations
81P05	General and philosophical questions in quantum theory
92B99	Mathematical biology in general

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