# Approximating integrals with respect to stationary probability measures of iterated function systems

## TL;DR

This paper introduces an efficient algorithm for approximating integrals with respect to stationary measures of iterated function systems, enabling better estimation of various mathematical properties like Hausdorff moments and Lyapunov exponents.

## Contribution

The paper presents a novel algorithm for fast approximation of integrals related to stationary measures of iterated function systems under specific conditions.

## Key findings

- Effective approximation of Hausdorff moments
- Accurate estimation of Wasserstein distances
- Reliable computation of Lyapunov exponents

## Abstract

We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the iterated function system and on the function that is being integrated. We apply this technique to estimate Hausdorff moments, Wasserstein distances and Lyapunov exponents of stationary probability measures.