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Mathematical Models of Discrete Self-Similarity

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  • F.M. Borodich

Abstract

Natural phenomena which exhibit discrete self-similarity are under consideration. Earlier, self-similarity of some non-smooth phenomena was studied using the concept of log-periodicity, however there was a gap in this field. Recently it was attempted to fill this gap by concentrating on the study of a new concept of parametric-homogeneity (PH) based on the use of discrete group of coordinate dilations. It is argued that parametric-homogeneity can be helpful in the modelling of self-similar non-smooth phenomena. Some models of natural phenomena which have PH-features are presented and some properties of PH-functions are discussed. As an example of practical usage of these functions, the phenomenon of seismic activation prior to a major earthquake is considered.

Suggested Citation

  • F.M. Borodich, 1999. "Mathematical Models of Discrete Self-Similarity," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 5(3), pages 245-258, September.
    • Handle: RePEc:taf:nmcmxx:v:5:y:1999:i:3:p:245-258
    DOI: 10.1076/mcmd.5.3.245.3680
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