Exact Dynamical Systems and the Frobenius-Perron Operator

Conditions are investigated which guarantee exactness for measurable maps on measure spaces. The main application is to certain piecewise continuous maps $T$ on $[0,1]$ for which $T’(0) > 1$. We assume $[0,1]$ can be broken into intervals on which $T$ is continuous and convex and at the left end of these intervals $T = 0$ and $dt/dx > 0$. Such maps have an invariant absolutely continuous density which is exact.