The beta transformation is the iterated map βx mod 1; it generates the base-β expansion of a
real number x. Every iterated piece-wise monotonic map is topologically conjugate to the …

The beta transformation is the iterated map $\beta x\mod1 $. The special case of $\beta= 2$
is known as the Bernoulli map, and is exactly solvable. The Bernoulli map provides a model …