Stock market crashes, Precursors and Replicas

We present an analysis of the time behavior of the S&P500 (Standard and Poors) New York stock exchange index before and after the October 1987 market crash and identify precursory patterns as well as aftershock signatures and characteristic oscillations of relaxation. Combined, they all suggest a picture of a kind of dynamical critical point, with characteristic log-periodic signatures, similar to what has been found recently for earthquakes. These observations are confirmed on other smaller crashes, and strengthen the view of the stockmarket as an example of a self-organizing cooperative system. R'esum'e Nous pr'esentons une analyse du comportement de l'indice boursier americain S&P500 avant et apr`es le crash d'octobre 1987. Nous identifions des motifs pr'ecurseurs ainsi que des oscillations de relaxation et des signatures de r'epliques apr`es le crash. Ces caract 'eristiques sugg`erent toutes ensembles que ce crash peut etre vu comme une sorte de point critique dynamique, poss'eda..