Given a vector field X on the real plane, we study the influence of the curvature of the orbits of ẋ = X⊥(x) in the stability of those of the system ẋ = X(x). We pay special attention to the case in which this curvature is negative in the whole plane. Under this assumption, we classify the possible critical points and give a criterion for a point to be globally asymptotically stable. In the general case, we also provide expressions for the first three derivatives of the Poincaré map associated to a periodic orbit in terms of geometrical quantities.
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - 1 Oct 1996|