Subpopulations Vector Spaces of Ordinal Patterns Reveal Symmetry Families in Experimental Time Series

We introduce a vector representation of subpopulations in the ordinal pattern description of observed time series as a technique to analyze previously observed correlations in these subpopulations. We show that a specific 3D projection of this vector space emphasizing time reversal symmetry reveals information about the phase space dynamics. In particular it helps us to identify families of chaos in specific locations of symmetry space. The trajectory in symmetry space encodes the evolution of phase space as a function of parameter. We discuss general consequences and specific applications of these observations.