Rigorous pointwise approximations for invariant densities of nonuniformly expanding maps

2013/01/17 by Bahsoun, Wael, Bose, Christopher, Duan, Yuejiao
#37A05 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1301.4033

Abstract

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^*⋅(ln m)/(m), where C^* is a computable fixed constant and m^-1 is the mesh size of the discretization.

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