Split-hyperbolicity in studying dynamical systems with hysteresis

Split-hyperbolicity was offered by A. Pokrovskii as an extension of the notions of "unsual" hyperbolicity for non-smooth maps. The nature of this concept makes it very useful in the study of systems with hysteresis. In this article we would like to survey recent results on split-hyperbolicity theory, and to outline its applications to the stabilisation of unstable orbits.