The goal of this review is to outline some unconventional ideas behind new paradigms in the modern theory of turbulence. Application of nonstandard, topological methods to describe the structural properties of the turbulent state is considered and the transition to kinetic equations in fractional derivatives for describing the microscopic behavior of a medium is examined. Central to the discussion is the concept of the percolation constant C ≈ 1.327..., a universal parameter describing the topology of nonequilibrium (quasi)stationary states in complex nonlinear dynamical systems allowing self-organized critical behavior. Much attention is given to the formation of power-law energy density spectra in turbulent media. A number of topical problems in modern cosmic electrodynamics, including the self-consistent fractal model of a turbulent current sheet, substorm dynamics, and the formation and dynamical evolution of large-scale magnetic fields in the solar photosphere and interplanetary space, are also discussed.

PACS: 05.40.−a, 05.45.Df, 05.65.+b, 94.30.−d (all) DOI: 10.1070/PU2004v047n08ABEH001705 URL: https://ufn.ru/en/articles/2004/8/a/ 000225645400001 Citation: Zelenyi L M, Milovanov A V "Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics" Phys. Usp. 47 749–788 (2004) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Зеленый Л М, Милованов А В «Фрактальная топология и странная кинетика: от теории перколяции к проблемам космической электродинамики» УФН 174 809–852 (2004); DOI: 10.3367/UFNr.0174.200408a.0809