Existence of homoclinic and heteroclinic connections in continuous piecewise linear systems

Abstract

In the present work, the existence of global connections in a continuous piecewise linear system is analytically proven. Concretely, by using a common technique we prove the existence of a pair of homoclinic connections and a reversible T-point heteroclinic cycle. The main ideas of this proof can be extended to other piecewise linear systems.