Low-dimensional dynamics in observables from complex and higher-dimensional systems

We analyze fluctuating observables of high-dimensional systems as the New York Stock Market S&P 500 index, the amino-acid sequence in the M. genitalium DNA, the maximum temperature of the San Francisco Bay area, and the toroidal magneto plasma potential. The probability measures of these fluctuations are obtained by the statistical analysis of a rescaling combination of the first Poincaré return time of a low-dimensional chaotic system. This result indicates that it is possible to use a measure of a low-dimensional chaotic attractor to describe a measure of these complex systems. Moreover, within this description we determine scaling power laws for average measurements of the analyzed fluctuations.