On complete chaotic maps with tent-map-like structures

A unimodal map f : [0, 1] → [0, 1] is said to be complete chaotic if it is both ergodic and chaotic in a probabilistic sense so as to preserve an absolutely continuous invariant measure. The sufficient conditions are provided to construct complete chaotic maps with the tent-map-like structures, that is, f(x) = 1 − 1 − 2g(x) , where g is an one-to-one onto map defined on [0, 1]. The simplicity and analytical characteristics of such chaotic maps simplify the calculations of various statistical properties of chaotic dynamics.