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Linear response for intermittent maps
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dc.contributor.author | Baladi, Viviane | |
dc.contributor.author | Todd, Michael John | |
dc.date.accessioned | 2017-02-23T00:32:26Z | |
dc.date.available | 2017-02-23T00:32:26Z | |
dc.date.issued | 2016-11 | |
dc.identifier | 207780558 | |
dc.identifier | 9f3ec5b0-fd15-49bf-b88e-9494674dada1 | |
dc.identifier | 84959134261 | |
dc.identifier | 000385162900006 | |
dc.identifier.citation | Baladi , V & Todd , M J 2016 , ' Linear response for intermittent maps ' , Communications in Mathematical Physics , vol. 347 , no. 3 , pp. 857-874 . https://doi.org/10.1007/s00220-016-2577-z | en |
dc.identifier.issn | 0010-3616 | |
dc.identifier.other | ORCID: /0000-0002-0042-0713/work/54181511 | |
dc.identifier.uri | https://hdl.handle.net/10023/10334 | |
dc.description.abstract | We consider the one parameter family α↦Tα (α∈[0,1)) of Pomeau-Manneville type interval maps Tα(x)=x(1+2αxα) for x∈[0,1/2) and Tα(x)=2x−1 for x∈[1/2,1], with the associated absolutely continuous invariant probability measure μα. For α∈(0,1), Sarig and Gouëzel proved that the system mixes only polynomially with rate n1−1/α (in particular, there is no spectral gap). We show that for any ψ∈Lq, the map α→∫10ψdμα is differentiable on [0,1−1/q), and we give a (linear response) formula for the value of the derivative. This is the first time that a linear response formula for the SRB measure is obtained in the setting of slowly mixing dynamics. Our argument shows how cone techniques can be used in this context. For α≥1/2 we need the n−1/α decorrelation obtained by Gouëzel under additional conditions. | |
dc.format.extent | 18 | |
dc.format.extent | 533556 | |
dc.language.iso | eng | |
dc.relation.ispartof | Communications in Mathematical Physics | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject.lcc | QA | en |
dc.title | Linear response for intermittent maps | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1007/s00220-016-2577-z | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2017-02-22 |
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