Science and Mathematics Faculty Presentations

Title

Chaos in Dendritic Julia Sets

Document Type

Conference Presentation

Conference/Event

Spring Topology and Dynamics Conference

Location

Waco, TX

Event Date

3-2016

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.

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