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Distributional Chaos in Dendritic Julia Sets
Summer Conference on Topology and its Application
  • Nathan Averbeck, Cedarville University
  • Brian E. Raines
Document Type
Conference Presentation
Galway, Ireland
Event Date
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.
Citation Information
Nathan Averbeck and Brian E. Raines. "Distributional Chaos in Dendritic Julia Sets" Summer Conference on Topology and its Application (2015)
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