  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.
