Peixoto's theorem

Peixoto's theorem

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.


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