{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:14:40Z","timestamp":1772288080260,"version":"3.50.1"},"reference-count":34,"publisher":"IOP Publishing","issue":"11","license":[{"start":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T00:00:00Z","timestamp":1570579200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T00:00:00Z","timestamp":1570579200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["SFRH\/BD\/93856\/2013"],"award-info":[{"award-number":["SFRH\/BD\/93856\/2013"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2019,11,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We consider one parameter families of vector fields introduced by Rovella, obtained through modifying the eigenvalues of the geometric Lorenz attractor, replacing the expanding condition on the eigenvalues of the singularity by a contracting one. We show that there is no statistical stability within the set of parameters for which there is a physical measure supported on the attractor. This is achieved obtaining a similar conclusion at the level of the corresponding one-dimensional contracting Lorenz maps.<\/jats:p>","DOI":"10.1088\/1361-6544\/ab2f48","type":"journal-article","created":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T05:13:15Z","timestamp":1570597995000},"page":"4413-4444","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Statistical instability for contracting Lorenz flows"],"prefix":"10.1088","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9241-5198","authenticated-orcid":false,"given":"Jos\u00e9 F","family":"Alves","sequence":"first","affiliation":[]},{"given":"Muhammad Ali","family":"Khan","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2019,10,9]]},"reference":[{"key":"nonab2f48bib001","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1088\/0951-7715\/17\/4\/004","type":"journal-article","article-title":"Strong statistical stability of non-uniformly expanding maps","volume":"17","author":"Alves","year":"2004","journal-title":"Nonlinearity"},{"key":"nonab2f48bib002","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/s002220000057","type":"journal-article","article-title":"SRB measures for partially hyperbolic systems whose central direction is mostly expanding","volume":"140","author":"Alves","year":"2000","journal-title":"Inventiones Math."},{"key":"nonab2f48bib003","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1016\/j.anihpc.2009.09.009","type":"journal-article","article-title":"Statistical stability for H\u00e9non maps of the Benedicks\u2013Carleson type","volume":"27","author":"Alves","year":"2010","journal-title":"Ann. Inst. Henri Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"key":"nonab2f48bib004","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s00220-010-1027-6","type":"journal-article","article-title":"Statistical stability and continuity of SRB entropy for systems with Gibbs\u2013Markov structures","volume":"296","author":"Alves","year":"2010","journal-title":"Commun. Math. Phys."},{"key":"nonab2f48bib005","doi-asserted-by":"publisher","first-page":"3527","DOI":"10.1088\/0951-7715\/25\/12\/3527","type":"journal-article","article-title":"Statistical stability and limit laws for Rovella maps","volume":"25","author":"Alves","year":"2012","journal-title":"Nonlinearity"},{"key":"nonab2f48bib006","article-title":"Statistical stability for Rovella flows","author":"Alves","year":"2019","type":"other"},{"key":"nonab2f48bib007","doi-asserted-by":"publisher","first-page":"219","DOI":"10.4064\/fm224-3-2","type":"journal-article","article-title":"Statistical stability of geometric Lorenz attractors","volume":"224","author":"Alves","year":"2014","journal-title":"Fund. Math."},{"key":"nonab2f48bib008","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0143385702000019","type":"journal-article","article-title":"Statistical stability for robust classes of maps with non-uniform expansion","volume":"22","author":"Alves","year":"2002","journal-title":"Ergod. Theor. Dynam. Syst."},{"key":"nonab2f48bib009","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/etds.2018.28","type":"journal-article","article-title":"On the statistical stability of Lorenz attractors with a C1+\u03b1 stable foliation","author":"Bahsoun","year":"2018","journal-title":"Ergod. Theor. Dynam. Syst."},{"key":"nonab2f48bib010","first-page":"1431","type":"other","article-title":"Analyticity of the SRB measure for holomorphic families of quadratic-like Collet\u2013Eckmann maps","volume":"137","author":"Baladi","year":"2009"},{"key":"nonab2f48bib011","doi-asserted-by":"publisher","first-page":"861","DOI":"10.24033\/asens.2179","type":"journal-article","article-title":"Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps","volume":"45","author":"Baladi","year":"2012","journal-title":"Ann. Sci. \u00c9c. Norm. Sup\u00e9r. (4)"},{"key":"nonab2f48bib012","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/1971367","type":"journal-article","article-title":"On iterations of 1\u2009\u2009\u2212\u2009\u2009ax2 on (\u22121,1)","volume":"122","author":"Benedicks","year":"1985","journal-title":"Ann. Math."},{"key":"nonab2f48bib013","doi-asserted-by":"publisher","first-page":"73","DOI":"10.2307\/2944326","type":"journal-article","article-title":"The dynamics of the H\u00e9non map","volume":"133","author":"Benedicks","year":"1991","journal-title":"Ann. Math."},{"key":"nonab2f48bib014","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/BF01389848","type":"journal-article","article-title":"The ergodic theory of Axiom A flows","volume":"29","author":"Bowen","year":"1975","journal-title":"Inventiones Math."},{"key":"nonab2f48bib015","volume":"vol 25","author":"De Melo","year":"2012","type":"book"},{"key":"nonab2f48bib016","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1088\/0951-7715\/18\/2\/019","type":"journal-article","article-title":"Continuity of SRB measure and entropy for Benedicks\u2013Carleson quadratic maps","volume":"18","author":"Freitas","year":"2005","journal-title":"Nonlinearity"},{"key":"nonab2f48bib017","doi-asserted-by":"publisher","first-page":"525","DOI":"10.4171\/PM\/1876","type":"journal-article","article-title":"Exponential decay of hyperbolic times for Benedicks\u2013Carleson quadratic maps","volume":"67","author":"Freitas","year":"2010","journal-title":"Port. Math."},{"key":"nonab2f48bib018","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/BF02684769","type":"journal-article","article-title":"Structural stability of Lorenz attractors","volume":"50","author":"Guckenheimer","year":"1979","journal-title":"Inst. Hautes \u00c9tudes Sci. Publ. Math."},{"key":"nonab2f48bib019","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/BF02096761","type":"journal-article","article-title":"Quadratic maps without asymptotic measure","volume":"127","author":"Hofbauer","year":"1990","journal-title":"Commun. Math. Phys."},{"key":"nonab2f48bib020","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/BF01667385","type":"journal-article","article-title":"Stochastic stability in some chaotic dynamical systems","volume":"94","author":"Keller","year":"1982","journal-title":"Monatsh. Math."},{"key":"nonab2f48bib021","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","type":"journal-article","article-title":"Deterministic non-periodic flow","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. Atmos. Sci."},{"key":"nonab2f48bib022","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/S0294-1449(00)00111-6","type":"journal-article","article-title":"Sinai-Ruelle-Bowen measures for contracting Lorenz maps and flows","volume":"17","author":"Metzger","year":"2000","journal-title":"Ann. Inst. Henri Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"key":"nonab2f48bib023","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/s002200000220","type":"journal-article","article-title":"Stochastic stability for contracting Lorenz maps and flows","volume":"212","author":"Metzger","year":"2000","journal-title":"Commun. Math. Phys."},{"key":"nonab2f48bib024","article-title":"Chaotic dynamics of quadratic maps","author":"Moreira","year":"1992","type":"other"},{"key":"nonab2f48bib025","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/BF01237679","type":"journal-article","article-title":"The dynamics of perturbations of the contracting Lorenz attractor","volume":"24","author":"Rovella","year":"1993","journal-title":"Bol. Soc. Brasil. Mat. (N.S.)"},{"key":"nonab2f48bib026","doi-asserted-by":"publisher","first-page":"619","DOI":"10.2307\/2373810","type":"journal-article","article-title":"A measure associated with axiom-A attractors","volume":"98","author":"Ruelle","year":"1976","journal-title":"Am. J. Math."},{"key":"nonab2f48bib027","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/BF02096659","type":"journal-article","article-title":"Regularity and other properties of absolutely continuous invariant measures for the quadratic family","volume":"150","author":"Rychlik","year":"1992","journal-title":"Commun. Math. Phys."},{"key":"nonab2f48bib028","first-page":"21","type":"journal-article","article-title":"Gibbs measures in ergodic theory","volume":"27","author":"Sinai","year":"1972","journal-title":"Usp. Mat. Nauk"},{"key":"nonab2f48bib029","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1007\/BF03025291","type":"journal-article","article-title":"Mathematical problems for the next century","volume":"20","author":"Smale","year":"1998","journal-title":"Math. Intelligencer"},{"key":"nonab2f48bib030","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02102427","type":"journal-article","article-title":"On continuity of Bowen\u2013Ruelle\u2013Sinai measures in families of one-dimensional maps","volume":"177","author":"Tsujii","year":"1996","journal-title":"Commun. Math. Phys."},{"key":"nonab2f48bib031","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1088\/0951-7715\/14\/2\/308","type":"journal-article","article-title":"Unfolding of chaotic unimodal maps and the parameter dependence of natural measures","volume":"14","author":"Thunberg","year":"2001","journal-title":"Nonlinearity"},{"key":"nonab2f48bib032","doi-asserted-by":"publisher","first-page":"1197","DOI":"10.1016\/S0764-4442(99)80439-X","type":"journal-article","article-title":"The Lorenz attractor exists","volume":"328","author":"Tucker","year":"1999","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"nonab2f48bib033","doi-asserted-by":"publisher","first-page":"1223","DOI":"10.1017\/S0143385700009895","type":"journal-article","article-title":"On the approximation of H\u00e9non-like attractors by homoclinic tangencies","volume":"15","author":"Ures","year":"1995","journal-title":"Ergod. Theor. Dynam. Syst."},{"key":"nonab2f48bib034","first-page":"214","type":"conference-proceedings","article-title":"H\u00e9non attractors: SBR measures and Dirac measures for sinks","author":"Ures","year":"1996"}],"container-title":["Nonlinearity"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ab2f48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ab2f48","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ab2f48","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ab2f48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ab2f48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ab2f48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ab2f48","content-type":"text\/html","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ab2f48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T13:48:50Z","timestamp":1770472130000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ab2f48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,9]]},"references-count":34,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,10,9]]},"published-print":{"date-parts":[[2019,11,1]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6544\/ab2f48","relation":{},"ISSN":["0951-7715","1361-6544"],"issn-type":[{"value":"0951-7715","type":"print"},{"value":"1361-6544","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,9]]},"assertion":[{"value":"Statistical instability for contracting Lorenz flows","name":"article_title","label":"Article Title"},{"value":"Nonlinearity","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2019 IOP Publishing Ltd & London Mathematical Society. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2019-05-13","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2019-07-04","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2019-10-09","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}