Fine structure and complex exponents in power law distributions from random maps
arXiv:cond-mat/9708220 · doi:10.1103/PhysRevE.57.120
Abstract
Discrete scale invariance (DSI) has recently been documented in time-to-failure rupture, earthquake processes and financial crashes, in the fractal geometry of growth processes and in random systems. The main signature of DSI is the presence of log-periodic oscillations correcting the usual power laws, corresponding to complex exponents. Log-periodic structures are important because they reveal the presence of preferred scaling ratios of the underlying physical processes. Here, we present new evidence of log-periodicity overlaying the leading power law behavior of probability density distributions of affine random maps with parametric noise. The log-periodicity is due to intermittent amplifying multiplicative events. We quantify precisely the progressive smoothing of the log-periodic structures as the randomness increases and find a large robustness. Our results provide useful markers for the search of log-periodicity in numerical and experimental data.
16 pages (double column RevTeX) with 16 (embedded eps) figures, to appear in Physical Review E
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