Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension.

ABSTRACT

We describe a fast and accurate method to compute the pressure and equilibrium states for maps of the interval T[0,1]-->[0,1] with respect to potentials phi[0,1]-->R. An approximate Ruelle-Perron-Frobenius operator is constructed and the pressure read off as the logarithm of the leading eigenvalue of this operator. By setting phi identical with 0, we recover the topological entropy. The conformal measure and the equilibrium state are computed as eigenvectors. Our approach is extremely efficient and very simple to implement. Rigorous convergence results are stated for piecewise expanding maps.