Border collision bifurcations in discontinuous one-dimensional linear-hyperbolic maps

In this paper we consider a discontinuous one-dimensional map, which is linear on one side of a generic point and hyperbolic on the other side, coming from economic applications. However this kind of piecewise smooth models is widely used also in other different applied contexts, and is characterized by border collision bifurcations. The simple formulation of the functions involved in the model allows for analytical results and the border collision bifurcations curves associated with the attracting cycles of the model are here determined. Also coexistence of two attracting cycles is shown to occur in a family of cycles of even period whose periodicity regions are overlapped in pair.