Korepanov, Alexey (2016) Linear response for intermittent maps with summable and nonsummable decay of correlations. Nonlinearity, 29 (6). pp. 1735-1754. doi:10.1088/0951-7715/29/6/1735 ISSN 0951-7715.

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Abstract

We consider a family of Pomeau–Manneville type interval maps ${{T}_{\alpha}}$ , parametrized by $\alpha \in (0,1)$ , with the unique absolutely continuous invariant probability measures ${{\nu}_{\alpha}}$ , and rate of correlations decay ${{n}^{1-1/\alpha}}$ . We show that despite the absence of a spectral gap for all $\alpha \in (0,1)$ and despite nonsummable correlations for $\alpha \geqslant 1/2$ , the map $\alpha \mapsto {\int}^{}\varphi \,\text{d}{{\nu}_{\alpha}}$ is continuously differentiable for $\varphi \in {{L}^{q}}\left[0,1\right]$ for q sufficiently large.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Differentiable dynamical systems
Journal or Publication Title:	Nonlinearity
Publisher:	Institute of Physics Publishing Ltd.
ISSN:	0951-7715
Official Date:	4 May 2016
Dates:	Date Event 4 May 2016 Published 4 May 2016 Available 7 April 2016 Accepted 4 September 2015 Submitted
Volume:	29
Number:	6
Page Range:	pp. 1735-1754
DOI:	10.1088/0951-7715/29/6/1735
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	1 August 2016
Date of first compliant Open Access:	4 May 2017
Funder:	European Research Council (ERC)
Grant number:	StochExtHomog (ERC AdG 320977)

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