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About: Peixoto's theorem     Goto   Sponge   NotDistinct   Permalink

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In the theory of dynamical systems, Peixoto theorem, proved by Maurício Peixoto, states that among all smooth flows on surfaces, i.e. compact two-dimensional manifolds, structurally stable systems may be characterized by the following properties: * The set of non-wandering points consists only of periodic orbits and fixed points. * The set of fixed points is finite and consists only of hyperbolic equilibrium points. * Finiteness of attracting or repelling periodic orbits. * Absence of saddle-to-saddle connections.