border collision bifurcations in one-dimensional linear-hyperbolic maps

in this paper we consider a continuous one-dimensional map, which is linear on one side of a generic kink point and hyperbolic on the other side. this kind of map is widely used in the applied context. due to the simple expression of the two functions involved, in particular cases it is possible to determine analytically the border collision bifurcation curves that characterize the dynamic behaviors of the model. in the more general model we show that the steps to be performed are the same, although the analytical expressions are not given in explicit form.