Математические основы фрактально-скейлингового метода в статистической радиофизике и приложениях

Abstract

The system of basic mathematical concepts and constructions underlying the modern global fractal-scaling method developed by the author is presented. An overview of the main results on the creation of new information technologies based on textures, fractals (multifractals), fractional operators, scaling effects and nonlinear dynamics methods obtained by the author and his students for more than 40 years (from 1979 to the present) at the V.A. Kotelnikov Institute of Radioengineering and Electronics of RAS. It is shown that, for the first time in the world, new dimensional and topological (and not energy!) Features or invariants were proposed and then effectively applied for problems in radio physics and radio electronics, which are combined under the generalized concept of "sample topology" ~ "fractal signature". The author discovered, proposed and substantiated a new type and new method of modern radar, namely, fractal-scaling or scale-invariant radar. It should be noted that fractal radars are, in fact, a necessary intermediate stage on the path of transition to cognitive radar and quantum radar.