Small Lipschitz Perturbation of Scalar Maps and Lyapunov Exponent for Lipschitz Maps

Abstract

In this paper we consider small Lipschitz perturbations for Lipschitz maps. We obtain conditions to ensure the permanence of fixed points (sink and source) for scalar Lipschitz maps without requiring differentiability, in a step norm weaker than the C 1 -norm and stronger than the C 0 -norm. Moreover, we also propose conditions in order to guarantee the permanence of periodic points. Additionally, we propose a new definition of Lyapunov exponent for Lipschitz maps which extends, in a natural way, the definition of Lyapunov exponent for differentiable maps.