# American Institute of Mathematical Sciences

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December  2016, 36(12): 6657-6668. doi: 10.3934/dcds.2016089

## Linear response in the intermittent family: Differentiation in a weighted $C^0$-norm

 1 Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU 2 Université de Brest, Laboratoire de Mathématiques de Bretagne Atlantique, CNRS UMR 6205, Brest, France

Received  January 2016 Revised  July 2016 Published  October 2016

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.
Citation: Wael Bahsoun, Benoît Saussol. Linear response in the intermittent family: Differentiation in a weighted $C^0$-norm. Discrete & Continuous Dynamical Systems, 2016, 36 (12) : 6657-6668. doi: 10.3934/dcds.2016089
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