Differential system

Fundamental theorem of flows

Let be differentiable. Let , be a neighbourhood of , for , and , . Then there exists a differentiable change of coördinates such that is equivalent to for .¹ #m/thm/dynamics/flow

That is to say flows in a neighbourhood of regular points are equivalent to parallel trajectories at constant velocity; the only interesting behaviour occurs in neighbourhoods of fixed points.

#state/tidy | #lang/en | #SemBr