DETECTING LOW-DIMENSIONAL CHAOS IN GEOPHYSICAL TIME-SERIES

Driven by the great appeal of the potential capability to reduce very, complex and highly erratic phenomenologies to simple deterministic an d predictable processes, much effort has been devoted to studying chao tic systems. Unfortunately, such studies have been essentially theoret ical, and the problem of detecting chaos in real time series has so fa r received little attention. As a consequence, the available technique s are fairly inefficient and are often misused. Furthermore, if detect ing chaos in real-time data would, in any case, be important from a ph ilosophical stand point, only low-dimensional chaos is of practical in terest, since it allows an effective short range predictability and co uld possibly also be modeled. A critical review of the available metho ds to detect chaos in a real series is presented together with a proce dure which is efficient in the presence of experimental errors and wit h relatively small sets of data. An application to the series of geoma gnetic inversions and to the eruptive activity of the Piton de la Four naise volcano, for which a chaotic dynamics appeared best documented, does not lead to detection of any low-dimensional chaos.