Chaotic functions on classical surfaces

There are various definitions of chaos in discrete dynamical systems. The LiYorke and Devaney's definitions of chaos are most widely used. The Devaney's definition of chaos is consist of three conditions namely, density of periodic points, topological transitivity and sensitively dependence on initial conditions. In this work firstly we give a theorem about the inducing of chaos conditions on quotient space.Then we construct chaotic functions on classical surfaces such as sphere, cylinder, torus, Mobius strip, Klein bottle and projective plan.