Peixoto's theorem
Template:Short description In the theory of dynamical systems, Peixoto's 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.
Moreover, they form an open set in the space of all flows endowed with C1 topology.
See also
References
- Jacob Palis, W. de Melo, Geometric Theory of Dynamical Systems. Springer-Verlag, 1982