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A rigorous computational approach to linear response

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journal contribution
posted on 22.11.2017, 10:08 authored by Wael BahsounWael Bahsoun, Stefano Galatolo, Isaia Nisoli, Xiaolong Niu
We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an algorithm to rigorously compute the linear response. We apply our results to expanding circle maps. In particular, we present examples where we compute, up to a pre-specified error in the L1-norm, the response of expanding circle maps under stochastic and deterministic perturbations. Moreover, we present an example where we compute, up to a pre-specified error in the L1-norm, the response of the intermittent family at the boundary; i.e., when the unperturbed system is the doubling map.

Funding

WB and SG would like to thank The Leverhulme Trust for supporting mutual research visits through the Network Grant IN-2014-021. The research of SG and IN is partially supported by EU Marie-Curie IRSES \Brazilian-European partnership in Dynamical Systems" (FP7-PEOPLE-2012-IRSES 318999 BREUDS). IN was partially supported by CNPq and FAPERJ. IN would like to thank the Department of Mathematics at Uppsala University and the support of the KAW grant 2013.0315.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Nonlinearity

Volume

31

Issue

3

Pages

1073 - 1109

Citation

BAHSOUN, W. ... et al., 2018. A rigorous computational approach to linear response. Nonlinearity, 31 (3), pp.1073-1109.

Publisher

IOP Publishing © IOP Publishing & London Mathematical Society

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

14/11/2017

Publication date

2018-02-12

Notes

This is the accepted version of the following article: BAHSOUN, W. ... et al., 2018. A rigorous computational approach to linear response. Nonlinearity, 31 (3), pp.1073-1109, which has been published in final form at https://doi.org/10.1088/1361-6544/aa9a88.

ISSN

0951-7715

eISSN

1361-6544

Language

en

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