SMOOTHNESS IMPLIES DETERMINISM - A METHOD TO DETECT IT IN TIME-SERIES

Continuity on an embedded phase space is enough to imply determinism i n time series. Also, it is possible to define infinitely many arbitrar y vector fields over an attractor. We exploit this arbitrariness to ge nerate a detector of smoothness and therefore of determinism in time s eries. We report results of numerical studies of both flow and map exa mples and of a chaotic experimental system.