Distributional Chaos in Dendritic Julia SetsSummer Conference on Topology and its Application
Document TypeConference Presentation
AbstractIn 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 InformationNathan Averbeck and Brian E. Raines. "Distributional Chaos in Dendritic Julia Sets" Summer Conference on Topology and its Application (2015)
Available at: http://works.bepress.com/nathan-averbeck/1/