Geometric methods for the study of local stability Original Research Article

A classical result by Hartman shows that near a hyperbolic equilibrium a system is (strongly) locally conjugate to its linearization. This result can be read “backwards”: near the equilibrium, a linear hyperbolic system is locally conjugate to its perturbations of order higher than one. We show a geometric method that allows us to extend this result to quasi-hyperbolic equilibria, provided the perturbation is of sufficiently high order. The proof of the main result uses Lewowicz’s method of Lyapunov functions of two variables.