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Linear response in the intermittent family: differentiation in a weighted C^0-norm
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 expandin...
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| Format: | Default Article |
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2016
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| Online Access: | https://hdl.handle.net/2134/23060 |
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| _version_ | 1818171661451526144 |
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| author | Wael Bahsoun Benoit Saussol |
| author_facet | Wael Bahsoun Benoit Saussol |
| author_sort | Wael Bahsoun (1258407) |
| collection | Figshare |
| description | 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. |
| format | Default Article |
| id | rr-article-9388844 |
| institution | Loughborough University |
| publishDate | 2016 |
| record_format | Figshare |
| spelling | rr-article-93888442016-12-31T00:00:00Z Linear response in the intermittent family: differentiation in a weighted C^0-norm Wael Bahsoun (1258407) Benoit Saussol (7162388) Other mathematical sciences not elsewhere classified Linear response Intermittent maps Mathematical Sciences not elsewhere classified 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. 2016-12-31T00:00:00Z Text Journal contribution 2134/23060 https://figshare.com/articles/journal_contribution/Linear_response_in_the_intermittent_family_differentiation_in_a_weighted_C_0-norm/9388844 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified Linear response Intermittent maps Mathematical Sciences not elsewhere classified Wael Bahsoun Benoit Saussol Linear response in the intermittent family: differentiation in a weighted C^0-norm |
| title | Linear response in the intermittent family: differentiation in a weighted C^0-norm |
| title_full | Linear response in the intermittent family: differentiation in a weighted C^0-norm |
| title_fullStr | Linear response in the intermittent family: differentiation in a weighted C^0-norm |
| title_full_unstemmed | Linear response in the intermittent family: differentiation in a weighted C^0-norm |
| title_short | Linear response in the intermittent family: differentiation in a weighted C^0-norm |
| title_sort | linear response in the intermittent family: differentiation in a weighted c^0-norm |
| topic | Other mathematical sciences not elsewhere classified Linear response Intermittent maps Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/23060 |