On the non-equivalence of observables in phase-space reconstructions from recorded time series.

*(English)*Zbl 0936.81014From the text: This paper intends to discuss and show that the ability of reconstructing the phase space of a system may depend critically on the obwservable being used. Such a dependence will be quantified by using an observability index in the case of well-known systems. The goal here is to clearly exhibit that all dynamical variables of the given system are not equivalent when their time evolutions are used as scalar time series to investigate the underlying dynamics. An explicit example is discussed in the case of the variables of the Rössler system for which the relative observability among the variables of this system is quantified by using the observability index. It will be shown that it is more difficult to obtain a model from the \(z\) variable than from the others as suggested by the observability index.

##### MSC:

81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |

37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |

37M10 | Time series analysis of dynamical systems |