Distributional Chaos in Dendritic and Circular Julia SetsJournal of Mathematical Analysis and Applications
AbstractIf 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: 1) for all t>0, , and 2) for some t>0, . 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,
- Scrambled set,
- Julia set,
Citation InformationNathan Averbeck and Brian E. Raines. "Distributional Chaos in Dendritic and Circular Julia Sets" Journal of Mathematical Analysis and Applications Vol. 428 Iss. 2 (2015) p. 951 - 958
Available at: http://works.bepress.com/nathan-averbeck/5/