  Hierarchy of one-parameter families of chaotic maps with an invariant measure
have been introduced, where their appropriate coupling has lead to the
generation of some coupled chaotic maps with an invariant measure. It is shown
that these chaotic maps (also the coupled maps) do not undergo any period
doubling or period-n-tupling cascade bifurcation to chaos, but they have either
single fixed point attractor at certain values of the parameters or they are
ergodic in the complementary region. Using the invariant measure or
Sinai-Rulle-Bowen measure the Kolmogrov-Sinai entropy of the chaotic maps
(coupled maps) have been calculated analytically, where the numerical
simulations support the results
