Axiom A

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', a many-body thermostatted system is approximated by an Anosov system.

This article is about a property of dynamical systems. For the property of arithmetical semigroups, see Abstract analytic number theory. For the axiom for posets, see Baumgartner's axiom.
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