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Title: Linear response in the intermittent family: differentiation in a weighted C^0-norm
Authors: Bahsoun, Wael
Saussol, Benoit
Keywords: Linear response
Intermittent maps
Issue Date: 2016
Publisher: © American Institute of Mathematical Sciences
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.
Abstract: 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.
Description: This paper is closed access until October 2017.
Sponsor: Leverhulme Trust Network Grant IN-2014-021
Version: Accepted for publication
DOI: 10.3934/dcds.2016089
URI: https://dspace.lboro.ac.uk/2134/23060
Publisher Link: http://dx.doi.org/10.3934/dcds.2016089
ISSN: 1078-0947
Appears in Collections:Closed Access (Maths)

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