LZ complexity in chaotic dynamical systems and the quasiperiodic Fibonacci sequence

The origin the concept of LZ compexity is in information science. Here we use this notion to characterize chaotic dynamical systems. We make contact with the usual characteristics of chaos, such as Lyapunov exponent and K-entropy. It is shown that for a two-dimensional system LZ complexity is as powerful as other characteristics. We also apply LZ complexity to the study of the quasiperiodic Fibonacci sequence. We prove a theorem about its LZ complexity and based upon it conclude its long range order.