Chaotic Feature of Extensive Cosmic Ray Air Showers

The fractal dimensionality in time series of air shower arriving time intervals(ASATs) is observed for cosmic rays of energies larger than 3 x 1014 eV . We found 9 cases each composed of 128 ASATs for low fractal dimension (minimum 1.3) and 256 ASATs for high fractal dimension (maximum 4.5). The Fourier power spectrum for the time series showing the lowest fractal dimension is characterized by some quasi periodic peaks with the peak tops enveloped with a smooth curve similar to the incommensurate chaos, differing from that given by the random data or the f-a noise data.