BAHSOUN, W., BOSE, C. and DUAN, Y., 2015. Rigorous pointwise approximations for invariant densities of non-uniformly expanding maps. Ergodic Theory and Dynamical Systems, 35 (4), pp. 1028 - 1044.
We 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∗⋅(lnm)/m, where C∗ is a computable fixed constant and m−1 is the mesh size of the discretization.
This article was published in the journal Ergodic Theory and Dynamical Systems and the definitive version is available at: http://dx.doi.org/10.1017/etds.2013.91