MAX PRINCIPLE AND UNIVERSAL SPECTRUM OF PERIODS: COMPLEMENTARY FRACTAL DISTRIBUTIONS AS CONSEQUENCE OF RATIONAL AND IRRATIONAL RELATIONS BETWEEN PARTS OF THE WHOLE SYSTEM

Abstract

The paper discusses the assumption that Mach principle should result in existence of a universal spectrum of periods. It is shown that fragments of such a spectrum were found in time series of fluctuations of various processes. A general approach is considered that demonstrates the emergence of discrete states in the spectra of periods, which is based on two basic concepts: resonance and roughness of a physical system. This approach leads to the existence of two complementary fractal distributions associated with sets of rational and irrational relations between the elements of the whole system. A brief review of works that also consider universal spectra of periods is given.