  We study the dynamics of hierarchy of piecewise maps generated by
one-parameter families of trigonometric chaotic maps and one-parameter families
of elliptic chaotic maps of $\mathbf{cn}$ and $\mathbf{sn}$ types, in detail.
We calculate the Lyapunov exponent and Kolmogorov-Sinai entropy of the these
maps with respect to control parameter. Non-ergodicity of these piecewise maps
is proven analytically and investigated numerically . The invariant measure of
these maps which are not equal to one or zero, appears to be characteristic of
non-ergodicity behavior. A quantity of interest is the Kolmogorov-Sinai
entropy, where for these maps are smaller than the sum of positive Lyapunov
exponents and it confirms the non-ergodicity of the maps.
