Barbour, A. D. Chance and chaos. (English) Zbl 0868.60005 Elem. Math. 51, No. 2, 57-63 (1996). By detailed consideration of the mapping \(h:[0,1]\to [0,1]\) defined by \[ h(x)= \min\{x/c,(1-x)/(1-c)\},\quad c\in(0,1), \] the author shows that chance and chaos may be seen as different aspects of the same phenomenon, in which case randomness may be used to explain chaos. A main ingredient in chaos, viz. unpredictability, is interpreted via Markov stationary chains, the reversal theorem being used to conclude that a “chaotic” sequence is mirrored by a “random” sequence. Reviewer: A.Dale (Durban) MSC: 60A10 Probabilistic measure theory 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior Keywords:chance; chaos; Markov chain; reversal theorem PDFBibTeX XMLCite \textit{A. D. Barbour}, Elem. Math. 51, No. 2, 57--63 (1996; Zbl 0868.60005) Full Text: EuDML