Shadowing with chain transitivity

A transitive dynamical system is either sensitive or has a dense set of equicontinuity points [E. Akin, J. Auslander, K. Berg, When is a transitive map chaotic, in: Convergence in Ergodic Theory and Probability, Walter de Gruyter & Co., 1996, pp. 25–40]. We show that if a chain transitive system has shadowing property then it is either sensitive or all points are equicontinuous.