document: Stock market dynamics We elucidate on several empirical statistical observations of stock market returns . Moreover , we find that these properties are recurrent and are also present in invariant measures of low-dimensional dynamical systems . Thus , we propose that the returns are modeled by the first Poincare return time of a low-dimensional chaotic trajectory . This modeling , which captures the recurrent properties of the return fluctuations , is able to predict well the evolution of the observed statistical quantities . In addition , it explains the reason for which stocks present simultaneously dynamical properties and high uncertainties . In our analysis , we use data from the S&P 500 index and the Brazilian stock Telebras
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