Entropy of n-Fold Compositions of the Tent Map

The tent map is a finite monotone map, that is, there is a finite number of intervals where is increasing or decreasing. Define to be the number of intervals such that , the function composed with itself times is monotone. Define the entropy to be . The entropy of the regular tent map is known to be , as the number of fixed points is . Looking at where the maximum occurs in the interval on the axis and at allows us to find the number of monotone intervals, which determines the entropy of the tent map with different peaks.