Regularization and singular perturbation techniques for non-smooth systems

This paper is concerned with some aspects of the qualitative-geometric theory of non-smooth systems. We present a survey of the state of the art on the connection between the regularization process of nonsmooth vector fields and the singular perturbation problems. As a matter of fact, the main results in our setting fill a gap between these areas. Exploiting such results, applications to constrained differential equations are discussed. (C) 2011 Elsevier B.V. All rights reserved.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP