Singular perturbation of relaxed periodic orbits (Q1088044)

The author investigates the conditions under which the differential of a Poincaré map \(P^{\epsilon}\) for a system \(\dot x=f(x,y)\), \(\epsilon\dot y=g(x,y)\) (where \(\epsilon \in {\mathbb{R}}^+\), \(x\in {\mathbb{R}}^ n\), \(y\in {\mathbb{R}}^ m)\) converges uniformly to the differntial of a Poincaré map \(P^ 0\) for a reduced system \(\dot x=f(x,y)\), \(0=g(x,y)\). It follows then that, for small \(\epsilon\), \(P^{\epsilon}\) is a contraction, providing the uniqueness of the periodic orbit.