High Quality Content by WIKIPEDIA articles! In mathematics, Smale`s axiom A defines a class of dynamical systems which have been extensively studied and whose dynamics is relatively well understood. A prominent example is the Smale horseshoe map. The term "axiom A" originates with Stephen Smale. The importance of such systems is demonstrated by the chaotic hypothesis, which states that, `for all practical purposes`, that a many-body thermostatted system is approximated by an Anosov system.