## Abstract

Using a special form of Ulam's method, we estimate the measure-theoretic entropy of a triple *(M,T,mu)*, where *M* is a smooth manifold, *T* is a *C^{1+gamma}* uniformly hyperbolic map, and *mu* is the unique physical measure of *T*.
With a few additional calculations, we also obtain numerical estimates of (i) the physical measure *mu*, (ii) the Lyapunov exponents of *T* with respect to *mu*, (iii) the rate of decay of correlations for *(T,mu)* with respect to *C^gamma* test functions, and (iv) the rate of escape (for repellors).
Four main situations are considered: *T* is everywhere expanding, *T* is everywhere hyperbolic (Anosov), *T* is hyperbolic on an attracting invariant set (Axiom A attractor), and *T* is hyperbolic on a non-attracting invariant set (Axiom A non-attractor/repellor).