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Presentation
Chaos in Dendritic Julia Sets
Spring Topology and Dynamics Conference
  • Nathan Averbeck, Cedarville University
  • Brian E. Raines
Document Type
Conference Presentation
Location
Waco, TX
Event Date
3-1-2016
Abstract

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 shift map σ on these dendrites exhibits various forms of chaos, including distributional chaos of the first type (DC1). 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. "Chaos in Dendritic Julia Sets" Spring Topology and Dynamics Conference (2016)
Available at: http://works.bepress.com/nathan-averbeck/2/