Chaos in dendritic and circular Julia sets.
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Averbeck, Nathan, 1985-
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We demonstrate the existence of various forms of chaos (including transitive distributional chaos, w-chaos, topological chaos, and exact Devaney chaos) on two families of abstract Julia sets: the dendritic Julia sets DT and the "circular" Julia sets ԐT , whose symbolic encoding was introduced by Stewart Baldwin. In particular, suppose one of the two following conditions hold: either fc has a Julia set which is a dendrite, or (provided that the kneading sequence of c is Г-acceptable) that fc has an attracting or parabolic periodic point. Then, by way of a conjugacy which allows us to represent these Julia sets symbolically, we prove that fc exhibits various forms of chaos.