The full tent map on the unit interval isIts two affine branches expand lengths by two, and it preserves Lebesgue measure.
Given a finite measurable partition of an interval, the itinerary of records which partition element contains each iterate . Prescribing a finite initial word defines an itinerary cylinder. For the full tent map, every length- binary cylinder has Lebesgue measure up to endpoint conventions, so its itinerary process is a fair i.i.d. Bernoulli process.
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The Tent map is a mathematical function that is often used in the study of chaotic systems in dynamical systems theory. It is a simple yet powerful example of how complicated behavior can arise from a deterministic system. The Tent map is typically defined over the interval \([0, 1]\) and is given by the following piecewise function: \[ T(x) = \begin{cases} 2x & \text{if } 0 \leq x < 0.