Mathematics – General Mathematics
Scientific paper
2010-01-10
Chaos, Solitons and Fractals, vol 28, issue 3, (2006), 581-589
Mathematics
General Mathematics
AMS-Latex 2e, 16 pages, no figures
Scientific paper
The origin of complex structures, randomness, and irreversibility are analyzed in the scale free SL(2,R) analysis, which is an extension of the ordinary analysis based on the recently uncovered scale free $C^{2^n-1}$ solutions to linear ordinary differential equations. The role of an intelligent decision making is discussed. We offer an explanation of the recently observed universal renormalization group dynamics at the edge of chaos in logistic maps. The present formalism is also applied to give a first principle explanation of 1/$f$ noise in electrical circuits and solid state devices. Its relevance to heavy tailed (hyperbolic) distributions is pointed out.
Prasad Datta Dhurjati
Raut Santanu
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