Writing the history of dynamical systems and chaos:: Longue duree and revolution, disciplines and cultures

Between the late 1960s and the beginning of the 1980s, the wide recognition that simple dynamical laws could give rise to complex behaviors was sometimes hailed as a true scientific revolution impacting several disciplines, for which a striking label was coined-"chaos." Mathematicians quickly pointed out that the purported revolution was relying on the abstract theory of dynamical systems founded in the late 19th century by Henri Poincare who had already reached a similar conclusion. In this paper. we flesh out the historiographical tensions arising from these confrontations: longue-duree history and revolution; abstract mathematics and the use of mathematical techniques in various other domains. After reviewing the historiography of dynamical systems theory from Poincare to the 1960s, we highlight the pioneering work of a few individuals (Steve Smale, Edward Lorenz, David Ruelle). We then go on to discuss the nature of the chaos phenomenon, which, we argue, was a conceptual reconfiguration as much as a sociodisciplinary convergence. (C) 2002 Elsevier Science (USA).