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dc.contributor.authorBruin, Henk
dc.contributor.authorTodd, Michael John
dc.date.accessioned2016-03-10T00:11:46Z
dc.date.available2016-03-10T00:11:46Z
dc.date.issued2015-09
dc.identifier.citationBruin , H & Todd , M J 2015 , ' Wild attractors and thermodynamic formalism ' , Monatshefte für Mathematik , vol. 178 , no. 1 , pp. 39-83 . https://doi.org/10.1007/s00605-015-0747-2en
dc.identifier.issn0026-9255
dc.identifier.otherPURE: 12702622
dc.identifier.otherPURE UUID: 609b41f0-6395-43b9-a8dc-2d8fe939df17
dc.identifier.otherScopus: 84924368242
dc.identifier.otherORCID: /0000-0002-0042-0713/work/54181506
dc.identifier.otherWOS: 000359830800002
dc.identifier.urihttp://hdl.handle.net/10023/8394
dc.descriptionMT was partially supported by NSF Grants DMS 0606343 and DMS 0908093.en
dc.description.abstractFibonacci unimodal maps can have a wild Cantor attractor, and hence be Lebesgue dissipative, depending on the order of the critical point. We present a one-parameter family ƒλ of countably piecewise linear unimodal Fibonacci maps in order to study the thermodynamic formalism of dynamics where dissipativity of Lebesgue (and conformal) measure is responsible for phase transitions. We show that for the potential φt = -t log |ƒλ'|, there is a unique phase transition at some t1 ≤ 1, and the pressure P(φt ) is analytic (with unique equilibrium state) elsewhere. The pressure is majorised by a non-analytic C∞ curve (with all derivatives equal to 0 at  t1 < 1) at the emergence of a wild attractor, whereas the phase transition at t1 = 1 can be of any finite order for those λ for which ƒλ is Lebesgue conservative. We also obtain results on the existence of conformal measures and equilibrium states, as well as the hyperbolic dimension and the dimension of the basin of ω(c).
dc.format.extent45
dc.language.isoeng
dc.relation.ispartofMonatshefte für Mathematiken
dc.rights© Springer-Verlag Wien 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/s00605-015-0747-2en
dc.subjectTransienceen
dc.subjectThermodynamic formalismen
dc.subjectInterval mapsen
dc.subjectMarkov chainsen
dc.subjectEquilibrium statesen
dc.subjectNon-uniform hyperbolicityen
dc.subject37E05en
dc.subject37D35en
dc.subject60J10en
dc.subject37D25en
dc.subject37A10en
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleWild attractors and thermodynamic formalismen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1007/s00605-015-0747-2
dc.description.statusPeer revieweden
dc.date.embargoedUntil2016-03-10


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