  We give hierarchy of one-parameter family F(a,x) of maps of the interval
[0,1] with an invariant measure. Using the measure, we calculate
Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent, of
these maps analytically, where the results thus obtained have been approved
with numerical simulation. In contrary to the usual one-parameter family of
maps such as logistic and tent maps, these maps do not possess period doubling
or period-n-tupling cascade bifurcation to chaos, but they have single fixed
point attractor at certain parameter values, where they bifurcate directly to
chaos without having period-n-tupling scenario exactly at these values of
parameter whose Lyapunov characteristic exponent begins to be positive.
