  For the first time we apply the methodologies of nonlinear analysis to
investigate atomic matter. We use these methods in the analysis of Atomic
Weights and of Mass Number of atomic nuclei. Using the AutoCorrelation Function
and Mutual Information we establish the presence of nonlinear effects in the
mechanism of increasing mass of atomic nuclei considered as a function of the
atomic number. We find that increasing mass is divergent, possibly chaotic. We
also investigate the possible existence of a Power Law for atomic nuclei and,
using also the technique of the variogram, we conclude that a fractal regime
could superintend to the mechanism of increasing mass for nuclei. Finally,
using the Hurst exponent, evidence is obtained that the mechanism of increasing
mass in atomic nuclei is in the fractional Brownian regime. The most
interesting results are obtained by using Recurrence Quantification Analysis
(RQA). New recurrences, psudoperiodicities, self-resemblance and class of
self-similarities are identified with values of determinism showing oscillating
values indicating the presence of more or less stability during the process of
increasing mass of atomic nuclei. In brief, new regimes of regularities are
identified for atomic nuclei that deserve to be studied by future researches.
In particular an accurate analysis of binding energy values by nonlinear
methods is further required.
