If x and y belong to a metric space X, we call (x, y) a DC1 scrambled pair for f : X → X if the following conditions hold:If D ⊂ X is an uncountable set such that every x, y ∈ D form a DC1 scrambled pair for f , we say f exhibits distributional chaos of type 1. If there exists t > 0 such that condition 2) holds for any distinct points x, y ∈ D, then the chaos is said to be uniform. A dendrite is a locally connected, uniquely arcwise connected, compact metric space. In this paper we show that a certain family of quadratic Julia sets (one that contains all the quadratic Julia sets which are dendrites and many others which contain circles) has uniform DC1 chaos.
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