Border Collision Bifurcations in n-Dimensional Piecewise Linear   Discontinuous Maps
  In this paper we report some important results that help in analizing the border collision bifurcations that occur in n-dimensional discontinuous maps. For this purpose, we use the piecewise linear approximation in the neighborhood of the plane of discontinuity. Earlier, Feigin had made a similar analysis for general n-dimensional piecewise smooth continuous maps. Proceeding along similar lines, we obtain the general conditions of existence of period-1 and period-2 fixed points before and after a border collision bifurcation. The application of the method is then illustrated using a specific example of a two-dimensional discontinuous map. 
Partha Sharathi Dutta, Bitihotra Routroy, Soumitro Banerjee and   S.S.Alam