Morse–Smale system

Summary

A Morse–Smale system is a smooth dynamical system whose non-wandering set consists of finitely many hyperbolic periodic orbits, with stable and unstable manifolds meeting transversally. These are the dynamical systems with the simplest possible recurrent behaviour. They are structurally stable, and on a compact manifold they have zero topological entropy. The gradient flow of a Morse function for a generic metric is Morse–Smale, which links them to Morse theory and Morse homology.