Rigorous computation of diffusion coefficients for expanding maps
type: Item
instance of: scholarly article
title: Rigorous computation of diffusion coefficients for expanding maps
zbMATH Open document ID: 1390.37069
published in: Journal of Statistical Physics
publication date: 2018-04-26T00:00:00Z
review text: This paper considers real analytic expanding interval maps. A method for the rigorous approximation of diffusion coefficients including error bounds was given by \textit{W. Bahsoun} et al. [J. Stat. Phys. 163, No. 6, 1486--1503 (2016; Zbl 1360.37177)] based on Ulam's method. Here the authors find another method for approximating diffusion coefficients using periodic points and the real analyticity. Their method has quadratic exponential convergence with rigorous error bounds and is illustrated with Lanford's map as an example.
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 37M25
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 6865059
zbMATH Keywords: diffusion coefficient
zbMATH Keywords: expanding map
zbMATH Keywords: ergodic theory
author: Oliver Jenkinson
author: Mark Pollicott
author: P. Vytnova
reviewed by: Steve Pederson
MaRDI profile type: Publication
full work available at URL: s10955-017-1930-8
OpenAlex ID: W2772320378
cites work: Q4101884
cites work: Rigorous approximation of diffusion coefficients for expanding maps
cites work: Q4341161
cites work: Q3908199
cites work: Q3274141
cites work: r-adic one-dimensional maps and the Euler summation formula
cites work: Classes of linear operators. Vol. I
cites work: Informal Remarks on the Orbit Structure of Discrete Approximations to Chaotic Maps
cites work: On the Existence of Invariant Measures for Piecewise Monotonic Transformations
cites work: Rigorous numerical investigation of the statistical properties of piecewise expanding maps. A feasibility study
cites work: Q3999409
cites work: Zeta-functions for expanding maps and Anosov flows
cites work: Q4185090
cites work: Composition operators and classical function theory
cites work: Q3857325
cites work: Q5511350
DOI: 10.1007/S10955-017-1930-8
description: scientific article; zbMATH DE number 6865059