{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T08:52:17Z","timestamp":1772268737844,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,2,28]],"date-time":"2012-02-28T00:00:00Z","timestamp":1330387200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Commun. Math. Phys."],"published-print":{"date-parts":[[2012,4]]},"DOI":"10.1007\/s00220-012-1445-8","type":"journal-article","created":{"date-parts":[[2012,2,27]],"date-time":"2012-02-27T05:20:08Z","timestamp":1330320008000},"page":"215-246","source":"Crossref","is-referenced-by-count":18,"title":["Robust Exponential Decay of Correlations for Singular-Flows"],"prefix":"10.1007","volume":"311","author":[{"given":"V\u00edtor","family":"Ara\u00fajo","sequence":"first","affiliation":[]},{"given":"Paulo","family":"Varandas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,2,28]]},"reference":[{"key":"1445_CR1","first-page":"336","volume":"234","author":"V.S. Afraimovich","year":"1977","unstructured":"Afraimovich V.S., Bykov V.V., Shil\u2019nikov L.P.: On the appearence and structure of the Lorenz attractor. Dokl. Acad. Sci. USSR 234, 336\u2013339 (1977)","journal-title":"Dokl. Acad. Sci. USSR"},{"issue":"2","key":"1445_CR2","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s002220000057","volume":"140","author":"J.F. Alves","year":"2000","unstructured":"Alves J.F., Bonatti C., Viana M.: SRB measures for partially hyperbolic systems whose central direction is mostly expanding. Invent. Math. 140(2), 351\u2013398 (2000)","journal-title":"Invent. Math."},{"issue":"3","key":"1445_CR3","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1017\/S0143385703000579","volume":"24","author":"J.F. Alves","year":"2004","unstructured":"Alves J.F., Luzzatto S., Pinheiro V.: Lyapunov exponents and rates of mixing for one-dimensional maps. Erg. Th. Dyn. Sys. 24(3), 637\u2013657 (2004)","journal-title":"Erg. Th. Dyn. Sys."},{"issue":"3","key":"1445_CR4","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s00574-007-0049-y","volume":"38","author":"V. Ara\u00fajo","year":"2007","unstructured":"Ara\u00fajo V.: Large deviations bound for semiflows over a non-uniformly expanding base. Bull. Braz. Math. Soc. (N.S.) 38(3), 335\u2013376 (2007)","journal-title":"Bull. Braz. Math. Soc. (N.S.)"},{"key":"1445_CR5","unstructured":"Araujo, V., Galatolo, S., Pacifico, M.J.: Decay of correlations of maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors. In preparation, 2011"},{"issue":"2","key":"1445_CR6","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s10955-006-9183-y","volume":"125","author":"V. Ara\u00fajo","year":"2006","unstructured":"Ara\u00fajo V., Pacifico M.J.: Large deviations for non-uniformly expanding maps. J. Stat. Phys. 125(2), 415\u2013457 (2006)","journal-title":"J. Stat. Phys."},{"key":"1445_CR7","unstructured":"Ara\u00fajo, V., Pacifico, M.J.: Three-dimensional flows. Volume 53 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]. Heidelberg: Springer, 2010, with a foreword by Marcelo Viana"},{"key":"1445_CR8","doi-asserted-by":"crossref","first-page":"2431","DOI":"10.1090\/S0002-9947-08-04595-9","volume":"361","author":"V. Ara\u00fajo","year":"2009","unstructured":"Ara\u00fajo V., Pujals E.R., Pacifico M.J., Viana M.: Singular-hyperbolic attractors are chaotic. Transactions of the A.M.S. 361, 2431\u20132485 (2009)","journal-title":"Transactions of the A.M.S."},{"key":"1445_CR9","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s10240-006-0001-5","volume":"104","author":"A. Avila","year":"2006","unstructured":"Avila A., Gou\u00ebzel S., Yoccoz J.-C.: Exponential mixing for the Teichm\u00fcller flow. Publ. Math. Inst. Hautes \u00c9tudes Sci. 104, 143\u2013211 (2006)","journal-title":"Publ. Math. Inst. Hautes \u00c9tudes Sci."},{"issue":"3","key":"1445_CR10","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1090\/S0002-9939-04-07671-3","volume":"133","author":"V. Baladi","year":"2005","unstructured":"Baladi V., Vall\u00e9e B.: Exponential decay of correlations for surface semi-flows without finite Markov partitions. Proc. Amer. Math. Soc. 133(3), 865\u2013874 (2005)","journal-title":"Proc. Amer. Math. Soc."},{"issue":"8","key":"1445_CR11","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1016\/S0764-4442(97)80131-0","volume":"325","author":"C. Bonatti","year":"1997","unstructured":"Bonatti C., Pumari\u00f1o A., Viana M.: Lorenz attractors with arbitrary expanding dimension. C. R. Acad. Sci. Paris S\u00e9r. I Math. 325(8), 883\u2013888 (1997)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"1445_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0081279","volume-title":"Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Volume 470 of Lect. Notes in Math","author":"R. Bowen","year":"1975","unstructured":"Bowen R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Volume 470 of Lect. Notes in Math. Springer Verlag, Berlin-Heidelberg-New York (1975)"},{"key":"1445_CR13","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BF01389848","volume":"29","author":"R. Bowen","year":"1975","unstructured":"Bowen R., Ruelle D.: The ergodic theory of Axiom A flows. Invent. Math. 29, 181\u2013202 (1975)","journal-title":"Invent. Math."},{"issue":"3","key":"1445_CR14","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1090\/S0894-0347-06-00528-5","volume":"19","author":"A.I. Bufetov","year":"2006","unstructured":"Bufetov A.I.: Decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations and the central limit theorem for the Teichm\u00fcller flow on the moduli space of abelian differentials. J. Amer. Math. Soc. 19(3), 579\u2013623 (2006)","journal-title":"J. Amer. Math. Soc."},{"issue":"2","key":"1445_CR15","doi-asserted-by":"crossref","first-page":"269","DOI":"10.2307\/121010","volume":"147","author":"N.I. Chernov","year":"1998","unstructured":"Chernov N.I.: Markov approximations and decay of correlations for Anosov flows. Ann. of Math. (2) 147(2), 269\u2013324 (1998)","journal-title":"Ann. of Math. (2)"},{"issue":"1","key":"1445_CR16","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/BF01215756","volume":"95","author":"P. Collet","year":"1984","unstructured":"Collet P., Epstein H., Gallavotti G.: Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties. Commun. Math. Phys. 95(1), 61\u2013112 (1984)","journal-title":"Commun. Math. Phys."},{"issue":"1","key":"1445_CR17","doi-asserted-by":"crossref","first-page":"159","DOI":"10.3934\/dcds.2006.15.159","volume":"15","author":"K. D\u00edaz-Ordaz","year":"2006","unstructured":"D\u00edaz-Ordaz K.: Decay of correlations for non-H\u00f6lder observables for one-dimensional expanding Lorenz-like maps. Disc. Cont. Dyn. Syst. 15(1), 159\u2013176 (2006)","journal-title":"Disc. Cont. Dyn. Syst."},{"issue":"2","key":"1445_CR18","doi-asserted-by":"crossref","first-page":"357","DOI":"10.2307\/121012","volume":"147","author":"D. Dolgopyat","year":"1998","unstructured":"Dolgopyat D.: On decay of correlations in Anosov flows. Ann. of Math. (2) 147(2), 357\u2013390 (1998)","journal-title":"Ann. of Math. (2)"},{"issue":"5","key":"1445_CR19","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1017\/S0143385798117431","volume":"18","author":"D. Dolgopyat","year":"1998","unstructured":"Dolgopyat D.: Prevalence of rapid mixing in hyperbolic flows. Erg. Th. Dyn. Sys. 18(5), 1097\u20131114 (1998)","journal-title":"Erg. Th. Dyn. Sys."},{"key":"1445_CR20","volume-title":"Measure theory and fine properties of functions. Studies in Advanced Mathematics","author":"L.C. Evans","year":"1992","unstructured":"Evans L.C., Gariepy R.F.: Measure theory and fine properties of functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FC (1992)"},{"key":"1445_CR21","doi-asserted-by":"crossref","first-page":"269","DOI":"10.4007\/annals.2007.166.269","volume":"166","author":"M. Field","year":"2007","unstructured":"Field M., Melbourne I., T\u00f6rok A.: Stability of mixing and rapid mixing for hyperbolic flows. Ann. Math. 166, 269\u2013291 (2007)","journal-title":"Ann. Math."},{"key":"1445_CR22","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1017\/S0143385709000856","volume":"30","author":"S. Galatolo","year":"2010","unstructured":"Galatolo S., Pacifico M.J.: Lorenz like flows: exponential decay of correlations for the poincar\u00e9 map, logarithm law, quantitative recurrence. Erg. Th. Dyn. Sys. 30, 703\u20131737 (2010)","journal-title":"Erg. Th. Dyn. Sys."},{"issue":"1","key":"1445_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.24033\/bsmf.2500","volume":"134","author":"S. Gou\u00ebzel","year":"2006","unstructured":"Gou\u00ebzel S.: Decay of correlations for nonuniformly expanding systems. Bull. Soc. Math. France 134(1), 1\u201331 (2006)","journal-title":"Bull. Soc. Math. France"},{"key":"1445_CR24","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/BF02684769","volume":"50","author":"J. Guckenheimer","year":"1979","unstructured":"Guckenheimer J., Williams R.F.: Structural stability of Lorenz attractors. Publ. Math. IHES 50, 59\u201372 (1979)","journal-title":"Publ. Math. IHES"},{"key":"1445_CR25","unstructured":"Hartman, P.: Ordinary differential equations. Volume 38 of Classics in Applied Mathematics. PA, Philadelphia: SIAM Soc. for Industrial and Applied Mathematics 2002, corrected reprint of the second (1982) edition Boston, MA; Birkh\u00e4user, with a foreword by Peter Bates"},{"key":"1445_CR26","doi-asserted-by":"crossref","unstructured":"Hirsch, M., Pugh, C., Shub, M.: Invariant manifolds. Volume 583 of Lect. Notes in Math. New York: Springer Verlag (1977)","DOI":"10.1007\/BFb0092042"},{"issue":"2","key":"1445_CR27","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1112\/jlms\/jdm060","volume":"76","author":"M. Holland","year":"2007","unstructured":"Holland M., Melbourne I.: Central limit theorems and invariance principles for Lorenz attractors. J. Lond. Math. Soc. (2) 76(2), 345\u2013364 (2007)","journal-title":"J. Lond. Math. Soc. (2)"},{"issue":"3","key":"1445_CR28","doi-asserted-by":"crossref","first-page":"1275","DOI":"10.4007\/annals.2004.159.1275","volume":"159","author":"C. Liverani","year":"2004","unstructured":"Liverani C.: On contact Anosov flows. Ann. of Math. (2) 159(3), 1275\u20131312 (2004)","journal-title":"Ann. of Math. (2)"},{"key":"1445_CR29","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","volume":"20","author":"E.N. Lorenz","year":"1963","unstructured":"Lorenz E.N.: Deterministic nonperiodic flow. J. Atmosph. Sci. 20, 130\u2013141 (1963)","journal-title":"J. Atmosph. Sci."},{"issue":"2","key":"1445_CR30","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s00220-005-1411-9","volume":"260","author":"S. Luzzatto","year":"2005","unstructured":"Luzzatto S., Melbourne I., Paccaut F.: The Lorenz attractor is mixing. Commun. Math. Phys. 260(2), 393\u2013401 (2005)","journal-title":"Commun. Math. Phys."},{"issue":"1","key":"1445_CR31","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s00220-002-0676-5","volume":"229","author":"I. Melbourne","year":"2002","unstructured":"Melbourne I., T\u00f6r\u00f6k A.: Central limit theorems and invariance principles for time-one maps of hyperbolic flows. Commun. Math. Phys. 229(1), 57\u201371 (2002)","journal-title":"Commun. Math. Phys."},{"key":"1445_CR32","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/BF02916712","volume":"144","author":"I. Melbourne","year":"2004","unstructured":"Melbourne I., T\u00f6r\u00f6k A.: Statistical limit theorems for suspension flows. Israel J. Math. 144, 191\u2013209 (2004)","journal-title":"Israel J. Math."},{"key":"1445_CR33","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1017\/S0143385707000995","volume":"28","author":"R. Metzger","year":"2008","unstructured":"Metzger R., Morales C.: Sectional-hyperbolic systems. Erg. Th. Dyn. Sys. 28, 1587\u20131597 (2008)","journal-title":"Erg. Th. Dyn. Sys."},{"issue":"2","key":"1445_CR34","doi-asserted-by":"crossref","first-page":"375","DOI":"10.4007\/annals.2004.160.375","volume":"160","author":"C.A. Morales","year":"2004","unstructured":"Morales C.A., Pacifico M.J., Pujals E.R.: Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers. Ann. of Math. 160(2), 375\u2013432 (2004)","journal-title":"Ann. of Math."},{"issue":"1","key":"1445_CR35","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10955-010-9939-2","volume":"139","author":"M.J. Pacifico","year":"2010","unstructured":"Pacifico M.J., Todd M.: Thermodynamic formalism for contracting Lorenz flows. J. Stat. Phys. 139(1), 159\u2013176 (2010)","journal-title":"J. Stat. Phys."},{"issue":"3","key":"1445_CR36","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/BF01388579","volume":"81","author":"M. Pollicott","year":"1985","unstructured":"Pollicott M.: On the rate of mixing of Axiom A flows. Invent. Math. 81(3), 413\u2013426 (1985)","journal-title":"Invent. Math."},{"issue":"3-4","key":"1445_CR37","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1007\/BF01049724","volume":"67","author":"M. Pollicott","year":"1992","unstructured":"Pollicott M.: Exponential mixing for the geodesic flow on hyperbolic three-manifolds. J. Stat. Phy. 67(3-4), 667\u2013673 (1992)","journal-title":"J. Stat. Phy."},{"issue":"2","key":"1445_CR38","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1017\/S0143385799120911","volume":"19","author":"M. Pollicott","year":"1999","unstructured":"Pollicott M.: On the mixing of Axiom A attracting flows and a conjecture of Ruelle. Erg. Th. Dyn. Sys. 19(2), 535\u2013548 (1999)","journal-title":"Erg. Th. Dyn. Sys."},{"key":"1445_CR39","first-page":"115","volume":"23","author":"C. Pugh","year":"1971","unstructured":"Pugh C., Shub M.: Ergodic elements of ergodic actions. Comp. Math. 23, 115\u2013122 (1971)","journal-title":"Comp. Math."},{"key":"1445_CR40","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/BF02020331","volume":"8","author":"A. Renyi","year":"1957","unstructured":"Renyi A.: Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar. 8, 477\u2013493 (1957)","journal-title":"Acta Math. Acad. Sci. Hungar."},{"key":"1445_CR41","unstructured":"Rokhlin, V.A.: On the fundamental ideas of measure theory. A. M. S. Transl. 10, 1\u201352 (1962); transl. from Mat. Sbornik 25, 107\u2013150 (1949)"},{"issue":"2","key":"1445_CR42","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/BF01237679","volume":"24","author":"A. Rovella","year":"1993","unstructured":"Rovella A.: The dynamics of perturbations of the contracting Lorenz attractor. Bull. Braz. Math. Soc. 24(2), 233\u2013259 (1993)","journal-title":"Bull. Braz. Math. Soc."},{"key":"1445_CR43","doi-asserted-by":"crossref","first-page":"619","DOI":"10.2307\/2373810","volume":"98","author":"D. Ruelle","year":"1976","unstructured":"Ruelle D.: A measure associated with Axiom A attractors. Amer. J. Math. 98, 619\u2013654 (1976)","journal-title":"Amer. J. Math."},{"issue":"4","key":"1445_CR44","first-page":"191","volume":"296","author":"D. Ruelle","year":"1983","unstructured":"Ruelle D.: Flots qui ne m\u00e9langent pas exponentiellement. C. R. Acad. Sci. Paris S\u00e9r. I Math. 296(4), 191\u2013193 (1983)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"1445_CR45","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1070\/RM1972v027n04ABEH001383","volume":"27","author":"Y. Sinai","year":"1972","unstructured":"Sinai Y.: Gibbs measures in ergodic theory. Russ. Math. Surv. 27, 21\u201369 (1972)","journal-title":"Russ. Math. Surv."},{"key":"1445_CR46","doi-asserted-by":"crossref","unstructured":"Tucker, W.: The Lorenz attractor exists. C. R. Acad. Sci. Paris, 328, S\u00e9rie I, 1197\u20131202 (1999)","DOI":"10.1016\/S0764-4442(99)80439-X"},{"key":"1445_CR47","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1007\/s10955-011-0392-7","volume":"146","author":"P. Varandas","year":"2012","unstructured":"Varandas P.: specification and large deviations for weak Gibbs measures. J. Stat. Phys. 146, 330\u2013358 (2012)","journal-title":"J. Stat. Phys."}],"updated-by":[{"DOI":"10.1007\/s00220-015-2478-6","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2015,10,19]],"date-time":"2015-10-19T00:00:00Z","timestamp":1445212800000}}],"container-title":["Communications in Mathematical Physics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00220-012-1445-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00220-012-1445-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00220-012-1445-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,24]],"date-time":"2019-06-24T15:03:15Z","timestamp":1561388595000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00220-012-1445-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,28]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["1445"],"URL":"https:\/\/doi.org\/10.1007\/s00220-012-1445-8","relation":{"correction":[{"id-type":"doi","id":"10.1007\/s00220-015-2478-6","asserted-by":"object"}]},"ISSN":["0010-3616","1432-0916"],"issn-type":[{"value":"0010-3616","type":"print"},{"value":"1432-0916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,28]]}}}