Centre
A centre is a fixed point enclosed in orbits which are neither stable nor unstable. More generally, the centre manifold of a fixed point consists of all orbits about the point which neither decay nor grow exponentially.
A linear centre is a fixed point with pure imaginary eigenvalues, while a nonlinear centre is a fixed point with the dynamics described above. The Hartman-Grobman theorem gives no guarantee that linear centres correspond to nonlinear centres in a nonlinear system. However, for a few special cases we can conclude on the existence of a nonlinear centre:
See also Periodic solution
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