MR3039719 Reviewed Wang, Lidong; Liu, Heng; Gao, Yuelin Chaos for discrete dynamical system. J. Appl. Math. 2013, Art. ID 212036, 4 pp. (Reviewer: Gaetana Gambino) 37D45

Abstract

In this paper the authors show the relation between the definitions of Li-Yorke chaos and distributional chaos in discrete dynamical systems. In particular, after listing the main definitions and reviewing the known results, the authors prove that: • a discrete dynamical system is chaotic in the sense of Martelli and Wiggins when it exhibits transitive distributional chaos; • a discrete dynamical system is distributively chaotic in a sequence when it is chaotic in the strong sense of Li-Yorke. Finally, the authors prove a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke.