Rigorous pointwise approximations for invariant densities of non-uniformly expanding maps

Abstract

AbstractWe use an Ulam-type discretization scheme to provide pointwise approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate invariant density converges pointwise to the true density at a rate ${C}^{\ast } \cdot (\ln m)/ m$, where ${C}^{\ast } $ is a computable fixed constant and ${m}^{- 1} $ is the mesh size of the discretization.