Dynamics MOC

Hartman-Grobman theorem

Let be differentiable. If is a fixed point such that the Jacobian matrix has only eigenvalues with non-zero real parts, then there exists a neighbourhood of in which the dynamics of is equivalent to the linear system . #m/thm/dynamics

Proof

#missing/proof No proof given in @walkerMATH3021NonlinearDynamics2021

Such points are called hyperbolic fixed points. See Linear stability analysis.


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