Chaos in Dendritic Julia Sets
Spring Topology and Dynamics Conference
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.
Averbeck, Nathan and Raines, Brian E., "Chaos in Dendritic Julia Sets" (2016). Science and Mathematics Faculty Presentations. 267.