Invariant Scrambled Sets And Distributional Chaos

摘要

In their famous paper 'Period three implies chaos', Li and Yorke started a study of a very important phenomena in dynamical systems (known presently under the name Li-Yorke chaos). Recently, it was proved by Du that an interval map f is turbulent if and only if there is an invariant scrambled set for f. We extend this approach and prove that exactly the same characterization is valid for distributional chaos.