An elementary way to rigorously estimate convergence to equilibrium and escape rates

TL;DR

This paper introduces an elementary, computer-assisted method to rigorously estimate convergence to equilibrium and escape rates in dynamical systems satisfying a Lasota-Yorke inequality, using transfer operator approximations.

Contribution

It provides a new, straightforward approach for obtaining explicit bounds on decay of correlations and escape rates through transfer operator approximations.

Findings

Successfully computes explicit bounds for convergence and escape rates.

Demonstrates the method with rigorous experiments and concrete results.

Applicable to systems satisfying a Lasota-Yorke inequality.

Abstract

We show an elementary method to have (finite time and asymptotic) computer assisted explicit upper bounds on convergence to equilibrium (decay of correlations) and escape rate for systems satisfying a Lasota Yorke inequality. The bounds are deduced by the ones of suitable approximations of the system's transfer operator. We also present some rigorous experiment showing the approach and some concrete result.