Matthew Williams

Stable Manifolds for Periodically Perturbed Maps and Application to Bipedal Locomotion

Abstract. We prove that if a certain entry in the map of the Hadamard–Perron theorem is [Formula: see text]-periodic in one of the variables, then the stable manifold guaranteed by the theorem is a graph of a [Formula: see text]-periodic function. As an application, we first extend the classical Levinson’s result abou...