After surveying several earlier definitions of "chaos" , this paper is devoted to presenting the recently introduced notion of distributional chaosto a non-specialist audience. It is shown that the theory of distributional chaos avoids various shortcomings of the earlier theories and that it allows one not only to distinguish between chaotic and non-chaotic behavior, but also to measure the actual extent of any existing chaotic behavior. The whole is illustrated with numerous examples.
"Distributional (and Other) Chaos and its Measurement." Real Anal. Exchange 26 (2) 495 - 524, 2000/2001.