Chance and chaos (Q1349444)

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.