Some Maps

This chapter deals with some important maps and their elementary properties. In particular, we are interested in finding fixed points, their stability behaviors, and formation of periodic cycles, stabilities of the periodic cycles, and bifurcation phenomena of some special maps. Maps and their compositions represent many natural phenomena or engineering processes. We shall introduce few particular bifurcations, viz., saddle-node (fold), period-doubling (flip), period-bubbling, pitchfork, transcritical bifurcations, and Neimark-Sacker codimension-2 bifurcation in this chapter.