Computing invariant densities and metric entropy

We present a method fur accurately computing the metric entropy (or, equivalently, the Lyapunov exponent) of the absolutely continuous invariant measure mu for a piecewise analytic expanding Markov map T of the interval. We construct atomic signed measures mu(M) supported on periodic orbits up to period M, and prove that integral log \T'\ d mu (M) --> (h) over bar (mu) super-exponentially fast, We illustrate our method with several examples.