This is based from the paper titled, "Chaos-Based Simultaneous Compression and Encryption for Hadoop" in Section 2.3.1 download link

The Authors say that given a symbolic sequence, it can be encoded into an initial condition by reverse interval mapping using the inverse map $f^{-1}_T(.)$. Then, starting from the initial condition, if the map $f_T(.)$ is iterated and the symbolic dynamics obtained by state space partition using the intervals computed from the encoding stage, we can obtain the same symbolic sequence.