Distributional Chaos in Dendritic Julia Sets
Summer Conference on Topology and its Application
In this talk, we will briefly discuss the set Λ and the notions of Λ-acceptable and (Λ, τ)-admissible sequences.
Baldwin has demonstrated that, for a given Λ-acceptable sequence τ, the set of (Λ, τ)-admissible sequences in Λ is a dendrite.
We show that the the shift map σ exhibits distributional chaos of the first type (DC1) on these dendrites. We have the following corollary: if f(z) = z2 + c, where c is complex, has a Julia set which is a dendrite, then f exhibits DC1.
Averbeck, Nathan and Raines, Brian E., "Distributional Chaos in Dendritic Julia Sets" (2015). Science and Mathematics Faculty Presentations. 269.