Rigorous approximation of diffusion coefficients for expanding maps

TL;DR

This paper presents a rigorous computational method using Ulam's approach to accurately approximate diffusion coefficients in uniformly expanding dynamical systems, demonstrated through Lanford's map.

Contribution

It introduces a new algorithm for rigorous approximation of diffusion coefficients in expanding maps, with practical implementation details.

Findings

Successful application to Lanford's map

Provides rigorous bounds on diffusion coefficients

Demonstrates effectiveness of Ulam's method

Abstract

We use Ulam's method to provide rigorous approximation of diffusion coefficients for uniformly expanding maps. An algorithm is provided and its implementation is illustrated using Lanford's map.