We consider the polynomials and rational maps as dynamical systems on the field Q_p of p-adic numbers. For a polynomial with coefficients in the ring of p-adic integers, the space is decomposed into minimal components and their attracting basins. For a transitive locally expanding polynomials, we can show that restricted to its Julia subset, it is conjugate to a subshift of finite type. For rational maps, we consider the homographic transformations on the projective line over Q_p. Such a system is conjugate to an affine map when it admits fixed points, and then has countablely many minimal components. When it has no fixed points, it is decomposed into finite many minimal components.