= Peixoto's theorem
{wiki=Peixoto's_theorem}
Peixoto's theorem is a result in the theory of dynamical systems, specifically regarding the behavior of flow on two-dimensional manifolds. Named after the Brazilian mathematician M. Peixoto, the theorem classifies the vector fields on a two-dimensional manifold in terms of their qualitative behavior. The central idea of Peixoto's theorem is to provide conditions under which the local behavior of a dynamical system can be classified.
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