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Chance and chaos. (English) Zbl 0868.60005

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
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