The Hierarchy Of Distributional Chaos

For each lambda is an element of [0, 1], lambda-power distributional chaos has been defined via Furstenberg families to strengthen distributional chaos. For the sake of distinguishing them, we present a class of dynamical systems, called wedge-shape systems. Through a thorough analysis of dynamical behaviors of all point-pairs, we show that wedge-shape systems can be lambda-power distributionally chaotic and admit no. lambda'-power distributionally scrambled pairs for any. lambda' is an element of [0, lambda). Then we unfold a picture of distributional chaos with rich hierarchical structures, which helps to improve our comprehension of the diversity of chaos.