A study on the Lyapunov exponents of sequences generated by the logistic map over integers

We are interested in the properties of sequences generated by the logistic map over integers. In the present paper, we give the Lyapunov exponents of the sequences generated by the map. Then, we confirm good correlations between a sign of the exponents and a few properties of randomness such as averages periods and link-lengths, and an occurrence rate of `0' bit in the generated sequence. Then, we prove that the exponent indicates stability of the sequence.