Smoothness Implies Determinism: A Method to Detect It in Time Series

Abstract

Continuity on an embedded phase space is enough to imply determinism in time series. Also, it is possible to define infinitely many arbitrary vector fields over an attractor. We exploit this arbitrariness to generate a detector of smoothness and therefore of determinism in time series. We report results of numerical studies of both flow and map examples and of a chaotic experimental system.