Distributional Chaos in Dendritic and Circular Julia Sets
Journal of Mathematical Analysis and Applications
If x and y belong to a metric space X , we call (x,y) a DC1 scrambled pair for f:X→X if the following conditions hold:
If D⊂X is an uncountable set such that every x,y∈D form a DC1 scrambled pair forf, we say f exhibits distributional chaos of type 1. If there exists t>0 such that condition 2) holds for any distinct points x,y∈D, then the chaos is said to be uniform. A dendrite is a locally connected, uniquely arcwise connected, compact metric space. In this paper we show that a certain family of quadratic Julia sets (one that contains all the quadratic Julia sets which are dendrites and many others which contain circles) has uniform DC1 chaos.
Schweizer–Smítal chaos, Distributional chaos, DC1, Scrambled set, Julia set, Dendrite
Averbeck, Nathan and Raines, Brian E., "Distributional Chaos in Dendritic and Circular Julia Sets" (2015). Science and Mathematics Faculty Publications. 353.