Limit cycles bifurcating from discontinuous centres

Abstract

In this article, we study limit cycles in discontinuous piecewise linear vector fields in R-2 and R-3. More precisely, we address the problem of understanding the dynamics around a degenerated two-fold singularity in R-2 and R-3, where it is also called T-singularity, which behave as discontinuous centres after suitable perturbations of the separation boundaries. We prove that, in both systems, it is possible to obtain k hyperbolic limit cycles bifurcating from these discontinuous centres, for any positive integer k. The same holds if k is infinity.