Energy-Variation Analysis and Orbit-Complexity Quantification

In state-recurrence analysis, recurrences are considered either in the space that constitutes of the observed quantities, or in an embedding space that is manufactured by time-delayed variables. An alternative approach is proposed here. In the so-called energy-variation analysis, the complexity of an orbit is quantified in terms of the statistics of the constant-speed geodesic condition. Energy-variation analysis requires significantly less operations than state-recurrence analysis, in particular, for multivariate time-series, while numerical experiments demonstrate that the resulting energy-recurrence matrix encodes information that is sufficient for quantifying the complexity of orbits.