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Linear response in the intermittent family: differentiation in a weighted C^0-norm

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journal contribution
posted on 04.11.2016, 11:35 by Wael BahsounWael Bahsoun, Benoit Saussol
We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our technique is based on inducing the non-uniformly expanding system to a uniformly expanding one, and on showing how the linear response formula of the non-uniformly expanding system is inherited from the linear response formula of the induced one. We apply this general technique to interval maps with a neutral fixed point (Pomeau-Manneville maps) to prove differentiability of the corresponding SRB measure. Our work covers systems that admit a finite SRB measure and it also covers systems that admit an infinite SRB measure. In particular, we obtain a linear response formula for both finite and infinite SRB measures. To the best of our knowledge, this is the first work that contains a linear response result for infinite measure preserving systems.

Funding

Leverhulme Trust Network Grant IN-2014-021

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Discrete and Continuous Dynamical Systems - Series A

Volume

36

Issue

12

Pages

6657-6668

Citation

BAHSOUN, W. and SAUSSOL, B., 2016. Linear response in the intermittent family: differentiation in a weighted C^0-norm. Discrete and Continuous Dynamical Systems - Series A, 36 (12), pp. 6657-6668.

Publisher

© American Institute of Mathematical Sciences

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/

Publication date

2016-12-31

Copyright date

2016

Notes

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series A following peer review. The definitive publisher-authenticated version BAHSOUN, W. and SAUSSOL, B., 2016. Linear response in the intermittent family: differentiation in a weighted C^0-norm. Discrete and Continuous Dynamical Systems - Series A, 36 (12), pp. 6657-6668. is available online at: http://dx.doi.org/10.3934/dcds.2016089

ISSN

1078-0947

eISSN

1553-5231

Language

en

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