The Lempel-Ziv complexity of 1/f spectral chaos and the infinite ergodic theory

A new large deviation property for the Lempel-Ziv complexity is numerically studied by using a one-dimesional non-hyperbolic "modified Bernoulli map", where the transition between stationary and non-stationary chaos is clearly observed. We will show that the Lempel-Ziv complexity and its fluctuations obey the universal scaling laws, and that the Lempel-Ziv complexity has the L¹-function property of the infinite ergodic theory. One of the most striking results is that the 1/f spectral process reveals the maximum diversity at the transition point from the stationary chaos to the non-stationary one.