Steady States and Cycles of a Difference Equation with Discontinuous Righthand Side
The article examines a scalar nonlinear difference equation with discontinuous right hand side on the interval. Under the condition of uniqueness and different arrangement with respect to the discontinuity of the attracting fixed points of functions describing the right-hand side to the left and to the right of the discontinuity, the domains of their attraction are established. In the absence of fixed points, continuity, and monotonicity of functions describing the right-hand side, conditions are obtained for the existence of attracting cycles with a period of two or more than two. It is shown that for convex or concave functions the domains of attraction of these cycles coincide with the interval on which the equation is defined.