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The self-affine mode of ice softening during friction is investigated within the rheological model for viscoelastic medium approximation. The different modes of ice rubbing, determined by formation of surface liquid-like layer, are studied. The analysis of time series of friction force is carried out, namely Fourier analysis, construction of autocorrelation and difference autocorrelation functions. The spectral power law is detected for modes of crystalline ice as well as of a mixture of stable ice and metastable softening. The self-similarity and aperiodic character of corresponding time series of friction force are proved.

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