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Linear response in the intermittent family: differentiation in a weighted C^0-norm
journal contribution
posted on 2016-11-04, 11:35 authored by Wael BahsounWael Bahsoun, Benoit SaussolWe 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 AVolume
36Issue
12Pages
6657-6668Citation
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 SciencesVersion
- 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
2016-12-31Copyright date
2016Notes
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.2016089ISSN
1078-0947eISSN
1553-5231Publisher version
Language
- en