THE ORDINAL STRUCTURE OF THE SIGNED SHIFT TRANSFORMATIONS

Abstract

Ordinal patterns bring in the dynamic novel aspects, difficult questions, and useful tools for entropy estimation, time series analysis and other applications. In [Amigó et al., 2008a], the structure of the ordinal patterns of the one- and two-sided shifts on N symbols was elucidated with great detail. The results are applied via order isomorphy to the ordinal structure of the sawtooth maps x ↦ Nx mod 1 and the baker map. In this paper, we generalize the technique employed there, to cope with the so-called signed shifts on N symbols and signed sawtooth maps.