ABSTRACT
The high sensitivity to initial conditions allowed us to conciliate, in certain cases, the concepts of irregularity and determinism. Typically, the output of an experiment is a set of (time-fluctuating) values for a scalar variable sampled at equally spaced intervals of time. The linearly optimized basis helps us to deal with noise reduction. Tradition, on the other hand, has ‘established’ time-delay imbeddings frequently as a first choice. Neither are these imbeddings the only possible ones, nor is there a need to restrict imbeddings to linear combinations of the measured variables. An alternative approach could be to try a statistical test for determinism. If the system is deterministic, a point in the imbedding should be enough to determine the next one in the time evolution of the system. Experimental time-series, however, are finite in both length and precision. The length of a time-series is usually severely limited by storage capabilities and the impossibility of maintaining a controlled environment for long times.
