Peixoto's theorem

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Devised by Maurício Peixoto, the theorem states that for dynamical systems on compact 2D manifolds, the structurally stable systems have the following properties:

• Finite number of hyperbolic equilibrium points.
• Finite number of attracting or repelling periodic orbits.
• No saddle-to-saddle connections.
• The set of non-wandering points consists only of periodic orbits and fixed points.