Bernoulli shift map

Despite bearing no direct relation to any physical dynamical system, the onedimensional discrete-time piecewise linear Bernoulli Shift map nonetheless displays many of the key mechanisms leading to deterministic chaos. The map is defined by (see figure 4.2) ... 

This binary decimal representation of xq should make obvious the reason why this map is named the Bernoulli shift. If xq < 1/2, then a = 0 if xq > 1/2 then ai = 1. Thus... 

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