Axiom A is a concept in dynamical systems introduced by mathematician Stephen Smale in the 1960s. It describes a class of systems that have certain hyperbolic properties, which means they exhibit chaotic behavior yet retain a structured dynamic. More specifically, Axiom A refers to a dynamical system where: 1. The system's phase space can be decomposed into an unstable manifold and stable manifold, making it possible to analyze orbits and their behavior under iteration.
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