title: 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.
authors.affiliation: School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia.
authors.forename: Gary
authors.initials: G
authors.lastname: Froyland
authors.forename: Rua
authors.initials: R
authors.lastname: Murray
authors.forename: Dalia
authors.initials: D
authors.lastname: Terhesiu