{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T21:40:51Z","timestamp":1776375651196,"version":"3.51.2"},"reference-count":36,"publisher":"American Mathematical Society (AMS)","issue":"11","license":[{"start":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T00:00:00Z","timestamp":1786579200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["UID\/MAT\/00144\/2019"],"award-info":[{"award-number":["UID\/MAT\/00144\/2019"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["CEECIND\/03721\/2017"],"award-info":[{"award-number":["CEECIND\/03721\/2017"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/MAT\/00144\/2019"],"award-info":[{"award-number":["UID\/MAT\/00144\/2019"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["CEECIND\/03721\/2017"],"award-info":[{"award-number":["CEECIND\/03721\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["UID\/MAT\/00144\/2019"],"award-info":[{"award-number":["UID\/MAT\/00144\/2019"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["CEECIND\/03721\/2017"],"award-info":[{"award-number":["CEECIND\/03721\/2017"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Trans. Amer. Math. Soc."],"abstract":"<p>\n                    In this paper we study the decay of correlations for Gibbs measures associated to codimension one Axiom A attractors for flows. We prove that a codimension one Axiom A attractor whose strong stable foliation is\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C Superscript 1 plus alpha\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>C<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">C^{1+\\alpha }<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and whose unstable subbundle is one-dimensional either has exponential decay of correlations with respect to all Gibbs measures associated to H\u00f6lder continuous potentials or its stable and unstable subbundles are jointly integrable. As a consequence, there exist\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C Superscript 1\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>C<\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">C^1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -open sets of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C Superscript 1 plus alpha\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>C<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">C^{1+\\alpha }<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -vector fields generating Axiom A flows (\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"alpha greater-than 0\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u03b1\n                              \n                            <\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\alpha &gt;0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ) having attractors so that they mix exponentially with respect to equilibrium states associated with H\u00f6lder continuous potentials.\n                  <\/p>","DOI":"10.1090\/tran\/9108","type":"journal-article","created":{"date-parts":[[2024,1,3]],"date-time":"2024-01-03T10:33:46Z","timestamp":1704278026000},"page":"7515-7554","source":"Crossref","is-referenced-by-count":0,"special_numbering":"1098","title":["Exponential decay of correlations for Gibbs measures on attractors of Axiom A flows"],"prefix":"10.1090","volume":"378","author":[{"given":"Diego","family":"Daltro","sequence":"first","affiliation":[]},{"given":"Paulo","family":"Varandas","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2025,8,13]]},"reference":[{"issue":"7","key":"1","doi-asserted-by":"publisher","first-page":"2971","DOI":"10.1090\/proc\/13055","article-title":"Open sets of axiom A flows with exponentially mixing attractors","volume":"144","author":"Ara\u00fajo, V.","year":"2016","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"issue":"11","key":"2","doi-asserted-by":"publisher","first-page":"2975","DOI":"10.1007\/s00023-016-0482-9","article-title":"Exponential decay of correlations for nonuniformly hyperbolic flows with a \ud835\udc36^{1+\ud835\udefc} stable foliation, including the classical Lorenz attractor","volume":"17","author":"Ara\u00fajo, Vitor","year":"2016","journal-title":"Ann. Henri Poincar\\'{e}","ISSN":"https:\/\/id.crossref.org\/issn\/1424-0637","issn-type":"print"},{"issue":"3","key":"3","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1007\/s00220-015-2471-0","article-title":"Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps","volume":"340","author":"Ara\u00fajo, V.","year":"2015","journal-title":"Comm. Math. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3616","issn-type":"print"},{"key":"4","unstructured":"V. Ara\u00fajo and M. J. Pacifico, Three-dimensional flows, 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], vol. 53, Springer, Heidelberg, 2010."},{"issue":"1","key":"5","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/s00220-012-1445-8","article-title":"Robust exponential decay of correlations for singular-flows","volume":"311","author":"Ara\u00fajo, V\u00edtor","year":"2012","journal-title":"Comm. Math. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3616","issn-type":"print"},{"issue":"104","key":"6","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/s10240-006-0001-5","article-title":"Exponential mixing for the Teichm\u00fcller flow","author":"Avila, Artur","year":"2006","journal-title":"Publ. Math. Inst. Hautes \\'{E}tudes Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0073-8301","issn-type":"print"},{"issue":"3","key":"7","doi-asserted-by":"publisher","first-page":"865","DOI":"10.1090\/S0002-9939-04-07671-3","article-title":"Exponential decay of correlations for surface semi-flows without finite Markov partitions","volume":"133","author":"Baladi, Viviane","year":"2005","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"key":"8","doi-asserted-by":"publisher","first-page":"429","DOI":"10.2307\/2373793","article-title":"Symbolic dynamics for hyperbolic flows","volume":"95","author":"Bowen, Rufus","year":"1973","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"key":"9","series-title":"Lecture Notes in Mathematics, Vol. 470","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0081279","volume-title":"Equilibrium states and the ergodic theory of Anosov diffeomorphisms","author":"Bowen, Rufus","year":"1975"},{"issue":"3","key":"10","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/BF01389848","article-title":"The ergodic theory of Axiom A flows","volume":"29","author":"Bowen, Rufus","year":"1975","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"2","key":"11","doi-asserted-by":"publisher","first-page":"1850006","DOI":"10.1142\/S0219493718500065","article-title":"The Dolgopyat inequality in bounded variation for non-Markov maps","volume":"18","author":"Bruin, Henk","year":"2018","journal-title":"Stoch. Dyn.","ISSN":"https:\/\/id.crossref.org\/issn\/0219-4937","issn-type":"print"},{"issue":"1","key":"12","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/s11856-017-1477-z","article-title":"Disintegration of invariant measures for hyperbolic skew products","volume":"219","author":"Butterley, Oliver","year":"2017","journal-title":"Israel J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-2172","issn-type":"print"},{"issue":"7","key":"13","doi-asserted-by":"publisher","first-page":"2253","DOI":"10.4171\/JEMS\/964","article-title":"Open sets of exponentially mixing Anosov flows","volume":"22","author":"Butterley, Oliver","year":"2020","journal-title":"J. Eur. Math. Soc. (JEMS)","ISSN":"https:\/\/id.crossref.org\/issn\/1435-9855","issn-type":"print"},{"issue":"2","key":"14","doi-asserted-by":"publisher","first-page":"269","DOI":"10.2307\/121010","article-title":"Markov approximations and decay of correlations for Anosov flows","volume":"147","author":"Chernov, N. I.","year":"1998","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"issue":"7","key":"15","doi-asserted-by":"publisher","first-page":"2137","DOI":"10.1007\/s00023-020-00991-5","article-title":"Exponential decay of correlations for Gibbs measures and semiflows over \ud835\udc36^{1+\ud835\udefc} piecewise expanding maps","volume":"22","author":"Daltro, Diego","year":"2021","journal-title":"Ann. Henri Poincar\\'{e}","ISSN":"https:\/\/id.crossref.org\/issn\/1424-0637","issn-type":"print"},{"issue":"2","key":"16","doi-asserted-by":"publisher","first-page":"357","DOI":"10.2307\/121012","article-title":"On decay of correlations in Anosov flows","volume":"147","author":"Dolgopyat, Dmitry","year":"1998","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"issue":"5","key":"17","doi-asserted-by":"publisher","first-page":"1097","DOI":"10.1017\/S0143385798117431","article-title":"Prevalence of rapid mixing in hyperbolic flows","volume":"18","author":"Dolgopyat, Dmitry","year":"1998","journal-title":"Ergodic Theory Dynam. Systems","ISSN":"https:\/\/id.crossref.org\/issn\/0143-3857","issn-type":"print"},{"issue":"1","key":"18","doi-asserted-by":"publisher","first-page":"269","DOI":"10.4007\/annals.2007.166.269","article-title":"Stability of mixing and rapid mixing for hyperbolic flows","volume":"166","author":"Field, Michael","year":"2007","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"issue":"2","key":"19","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1215\/00127094-2009-011","article-title":"Local limit theorem for nonuniformly partially hyperbolic skew-products and Farey sequences","volume":"147","author":"Gou\u00ebzel, S\u00e9bastien","year":"2009","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"},{"issue":"1","key":"20","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1017\/etds.2017.25","article-title":"Quantitative Pesin theory for Anosov diffeomorphisms and flows","volume":"39","author":"Gou\u00ebzel, S\u00e9bastien","year":"2019","journal-title":"Ergodic Theory Dynam. Systems","ISSN":"https:\/\/id.crossref.org\/issn\/0143-3857","issn-type":"print"},{"issue":"3","key":"21","doi-asserted-by":"publisher","first-page":"1275","DOI":"10.4007\/annals.2004.159.1275","article-title":"On contact Anosov flows","volume":"159","author":"Liverani, Carlangelo","year":"2004","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"key":"22","doi-asserted-by":"publisher","first-page":"729","DOI":"10.2307\/2373755","article-title":"Anosov flows","volume":"94","author":"Plante, Joseph F.","year":"1972","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"issue":"1","key":"23","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1017\/S0143385700002327","article-title":"A complex Ruelle-Perron-Frobenius theorem and two counterexamples","volume":"4","author":"Pollicott, Mark","year":"1984","journal-title":"Ergodic Theory Dynam. Systems","ISSN":"https:\/\/id.crossref.org\/issn\/0143-3857","issn-type":"print"},{"issue":"3","key":"24","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1007\/BF01388579","article-title":"On the rate of mixing of Axiom A flows","volume":"81","author":"Pollicott, Mark","year":"1985","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"2","key":"25","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1017\/S0143385799120911","article-title":"On the mixing of Axiom A attracting flows and a conjecture of Ruelle","volume":"19","author":"Pollicott, Mark","year":"1999","journal-title":"Ergodic Theory Dynam. Systems","ISSN":"https:\/\/id.crossref.org\/issn\/0143-3857","issn-type":"print"},{"issue":"5","key":"26","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1353\/ajm.1998.0041","article-title":"Exponential error terms for growth functions on negatively curved surfaces","volume":"120","author":"Pollicott, Mark","year":"1998","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"key":"27","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1007\/BF02771776","article-title":"Markov partitions for Anosov flows on \ud835\udc5b-dimensional manifolds","volume":"15","author":"Ratner, M.","year":"1973","journal-title":"Israel J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-2172","issn-type":"print"},{"issue":"3","key":"28","doi-asserted-by":"publisher","first-page":"619","DOI":"10.2307\/2373810","article-title":"A measure associated with axiom-A attractors","volume":"98","author":"Ruelle, David","year":"1976","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"issue":"4","key":"29","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1142\/9789812833709_0024","article-title":"Flots qui ne m\u00e9langent pas exponentiellement","volume":"296","author":"Ruelle, David","year":"1983","journal-title":"C. R. Acad. Sci. Paris S\\'{e}r. I Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0249-6291","issn-type":"print"},{"issue":"4","key":"30","first-page":"21","article-title":"Gibbs measures in ergodic theory","volume":"27","author":"Sina\u012d, Ja. G.","year":"1972","journal-title":"Uspehi Mat. Nauk","ISSN":"https:\/\/id.crossref.org\/issn\/0042-1316","issn-type":"print"},{"issue":"4","key":"31","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1088\/0951-7715\/24\/4\/005","article-title":"Spectra of Ruelle transfer operators for axiom A flows","volume":"24","author":"Stoyanov, Luchezar","year":"2011","journal-title":"Nonlinearity","ISSN":"https:\/\/id.crossref.org\/issn\/0951-7715","issn-type":"print"},{"issue":"2","key":"32","doi-asserted-by":"publisher","first-page":"391","DOI":"10.3934\/dcds.2013.33.391","article-title":"Pinching conditions, linearization and regularity of axiom A flows","volume":"33","author":"Stoyanov, Luchezar","year":"2013","journal-title":"Discrete Contin. Dyn. Syst.","ISSN":"https:\/\/id.crossref.org\/issn\/1078-0947","issn-type":"print"},{"issue":"1404","key":"33","isbn-type":"print","doi-asserted-by":"publisher","first-page":"v+121","DOI":"10.1090\/memo\/1404","article-title":"Spectral properties of Ruelle transfer operators for regular Gibbs measures and decay of correlations for contact Anosov flows","volume":"283","author":"Stoyanov, Luchezar","year":"2023","ISBN":"https:\/\/id.crossref.org\/isbn\/9781470456252","journal-title":"Mem. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-9266","issn-type":"print"},{"issue":"1","key":"34","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1017\/S0143385707000430","article-title":"Decay of correlations in suspension semi-flows of angle-multiplying maps","volume":"28","author":"Tsujii, Masato","year":"2008","journal-title":"Ergodic Theory Dynam. Systems","ISSN":"https:\/\/id.crossref.org\/issn\/0143-3857","issn-type":"print"},{"issue":"2","key":"35","doi-asserted-by":"publisher","first-page":"757","DOI":"10.2969\/jmsj\/07027595","article-title":"Exponential mixing for generic volume-preserving Anosov flows in dimension three","volume":"70","author":"Tsujii, Masato","year":"2018","journal-title":"J. Math. Soc. Japan","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5645","issn-type":"print"},{"issue":"1","key":"36","doi-asserted-by":"publisher","first-page":"65","DOI":"10.4007\/annals.2023.197.1.2","article-title":"Smooth mixing Anosov flows in dimension three are exponentially mixing","volume":"197","author":"Tsujii, Masato","year":"2023","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"}],"container-title":["Transactions of the American Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/tran\/2025-378-11\/S0002-9947-2025-09108-6\/tran9108_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/www.ams.org\/tran\/2025-378-11\/S0002-9947-2025-09108-6\/S0002-9947-2025-09108-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T20:41:05Z","timestamp":1776372065000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/tran\/2025-378-11\/S0002-9947-2025-09108-6\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,13]]},"references-count":36,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["S0002-9947-2025-09108-6"],"URL":"https:\/\/doi.org\/10.1090\/tran\/9108","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6850","0002-9947"],"issn-type":[{"value":"1088-6850","type":"electronic"},{"value":"0002-9947","type":"print"}],"subject":[],"published":{"date-parts":[[2025,8,13]]}}}