Fractal analysis for low temperature physics

Abstract

A short review of existing methods of monofractal analysis proposed for low temperature physics investigations is presented. Based on the nature of the algorithms used, a new classification of modern monofractal analysis methods is proposed. The properties, the advantages and the disadvantages of these methods are considered. An important new concept of second-order fractals is introduced. Using the set of simple deterministic theoretical models of both the second-order fractal signals created especially for this and the traditional fractal signals, the results of their comparison based on the wavelet analysis are shown. The peculiarities of the second-order fractals are discussed.