{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T22:27:36Z","timestamp":1769207256628,"version":"3.49.0"},"reference-count":24,"publisher":"IOP Publishing","issue":"34","license":[{"start":{"date-parts":[[2021,8,4]],"date-time":"2021-08-04T00:00:00Z","timestamp":1628035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2021,8,4]],"date-time":"2021-08-04T00:00:00Z","timestamp":1628035200000},"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":["PTDC\/MAT-PUR\/28177\/2017"],"award-info":[{"award-number":["PTDC\/MAT-PUR\/28177\/2017"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["J. Phys. A: Math. Theor."],"published-print":{"date-parts":[[2021,8,27]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We analyse the existence of limiting laws of rare events for dynamically generated stochastic processes. We consider two-dimensional dynamical systems and observable functions maximised on Cantor dust sets and prove the existence of distributional limits for the partial maxima. We show how the extremal index, measuring the degree of clustering of rare events, is linked to the compatibility between the dynamics and the fractal structure of the maximal sets.<\/jats:p>","DOI":"10.1088\/1751-8121\/ac16c6","type":"journal-article","created":{"date-parts":[[2021,7,21]],"date-time":"2021-07-21T18:42:57Z","timestamp":1626892977000},"page":"345202","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Rare events for product fractal sets\n                    <sup>*<\/sup>"],"prefix":"10.1088","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7307-3441","authenticated-orcid":false,"given":"Ana Cristina Moreira","family":"Freitas","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0868-2654","authenticated-orcid":false,"given":"Jorge Milhazes","family":"Freitas","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0270-7045","authenticated-orcid":false,"given":"Jorge Valentim","family":"Soares","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2021,8,4]]},"reference":[{"key":"aac16c6bib1","doi-asserted-by":"publisher","first-page":"670","DOI":"10.1112\/jlms.12332","type":"journal-article","article-title":"Dynamical counterexamples regarding the extremal index and the mean of the limiting cluster size distribution","volume":"102","author":"Abadi","year":"2020","journal-title":"J. Lond. Math. Soc."},{"key":"aac16c6bib2","doi-asserted-by":"publisher","first-page":"8229","DOI":"10.1090\/tran\/2015-367-11","type":"journal-article","article-title":"Laws of rare events for deterministic and random dynamical systems","volume":"367","author":"Ayta\u00e7","year":"2015","journal-title":"Trans. Am. Math. Soc."},{"key":"aac16c6bib3","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.physd.2015.10.002","type":"journal-article","article-title":"Clustering of extreme events created by multiple correlated maxima","volume":"315","author":"Azevedo","year":"2016","journal-title":"Physica D"},{"key":"aac16c6bib4","doi-asserted-by":"publisher","first-page":"1244","DOI":"10.1007\/s10955-017-1767-1","type":"journal-article","article-title":"Extreme value laws for dynamical systems with countable extremal sets","volume":"167","author":"Azevedo","year":"2017","journal-title":"J. Stat. Phys."},{"key":"aac16c6bib5","author":"Boyarsky","year":"1997","type":"book"},{"key":"aac16c6bib6","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2019.06.009","type":"journal-article","article-title":"Generalized dimensions, large deviations and the distribution of rare events","volume":"400","author":"Caby","year":"2019","journal-title":"Physica D"},{"key":"aac16c6bib7","article-title":"Extremes and extremal indices for level set observables on hyperbolic systems","author":"Carney","year":"2019","type":"preprint"},{"key":"aac16c6bib8","author":"Falconer","year":"2003","edition":"2nd edn","type":"book"},{"key":"aac16c6bib9","doi-asserted-by":"publisher","first-page":"1316","DOI":"10.1038\/s41467-019-09305-8","type":"journal-article","article-title":"The hammam effect or how a warm ocean enhances large scale atmospheric predictability","volume":"10","author":"Faranda","year":"2019","journal-title":"Nat. Commun."},{"key":"aac16c6bib10","doi-asserted-by":"publisher","first-page":"3326","DOI":"10.1088\/1361-6544\/aabc8e","type":"journal-article","article-title":"Extreme value theory for synchronization of coupled map lattices","volume":"31","author":"Faranda","year":"2018","journal-title":"Nonlinearity"},{"key":"aac16c6bib11","doi-asserted-by":"publisher","first-page":"713","DOI":"10.5194\/npg-24-713-2017","type":"journal-article","article-title":"Dynamical properties and extremes of northern hemisphere climate fields over the past 60 years","volume":"24","author":"Faranda","year":"2017","journal-title":"Nonlinear Process. Geophys."},{"key":"aac16c6bib12","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.119.014502","type":"journal-article","article-title":"Stochastic chaos in a turbulent swirling flow","volume":"119","author":"Faranda","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"aac16c6bib13","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s00220-020-03794-1","type":"journal-article","article-title":"Rare events for Cantor target sets","volume":"378","author":"Freitas","year":"2020","journal-title":"Commun. Math. Phys."},{"key":"aac16c6bib14","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1007\/s10955-010-0096-4","type":"journal-article","article-title":"Extreme value laws in dynamical systems for non-smooth observations","volume":"142","author":"Freitas","year":"2011","journal-title":"J. Stat. Phys."},{"key":"aac16c6bib15","doi-asserted-by":"publisher","first-page":"2626","DOI":"10.1016\/j.aim.2012.07.029","type":"journal-article","article-title":"The extremal index, hitting time statistics and periodicity","volume":"231","author":"Freitas","year":"2012","journal-title":"Adv. Math."},{"key":"aac16c6bib16","doi-asserted-by":"publisher","first-page":"3463","DOI":"10.1016\/j.spa.2016.05.001","type":"journal-article","article-title":"Rare events for the Manneville\u2013Pomeau map","volume":"126","author":"Freitas","year":"2016","journal-title":"Stoch. Process. Appl."},{"key":"aac16c6bib17","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1090\/s0002-9947-2011-05271-2","type":"journal-article","article-title":"Extreme value theory for non-uniformly expanding dynamical systems","volume":"364","author":"Holland","year":"2012","journal-title":"Trans. Am. Math. Soc."},{"key":"aac16c6bib18","doi-asserted-by":"publisher","first-page":"2043","DOI":"10.1214\/aos\/1176349409","type":"journal-article","article-title":"Extremal index estimation for a weakly dependent stationary sequence","volume":"21","author":"Hsing","year":"1993","journal-title":"Ann. Stat."},{"key":"aac16c6bib19","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1080\/14689367.2011.653329","type":"journal-article","article-title":"Rare events, exponential hitting times and extremal indices via spectral perturbation","volume":"27","author":"Keller","year":"2012","journal-title":"Dyn. Syst."},{"key":"aac16c6bib20","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.122.158701","type":"journal-article","article-title":"Transitions across melancholia states in a climate model: reconciling the deterministic and stochastic points of view","volume":"122","author":"Lucarini","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"aac16c6bib21","author":"Lucarini","year":"2016","type":"book"},{"key":"aac16c6bib22","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/49\/37\/374001","type":"journal-article","article-title":"Extreme value laws for fractal intensity functions in dynamical systems: Minkowski analysis","volume":"49","author":"Mantica","year":"2016","journal-title":"J. Phys. A: Math. Theor."},{"key":"aac16c6bib23","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1214\/aop\/1176992270","type":"journal-article","article-title":"Extreme values for stationary and Markov sequences","volume":"15","author":"O\u2019Brien","year":"1987","journal-title":"Ann. Probab."},{"key":"aac16c6bib24","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/bf02773219","type":"journal-article","article-title":"Absolutely continuous invariant measures for multidimensional expanding maps","volume":"116","author":"Saussol","year":"2000","journal-title":"Isr. J. Math."}],"container-title":["Journal of Physics A: Mathematical and Theoretical"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ac16c6","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ac16c6\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ac16c6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ac16c6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ac16c6\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ac16c6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ac16c6\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ac16c6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T13:51:46Z","timestamp":1765029106000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ac16c6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,4]]},"references-count":24,"journal-issue":{"issue":"34","published-online":{"date-parts":[[2021,8,4]]},"published-print":{"date-parts":[[2021,8,27]]}},"URL":"https:\/\/doi.org\/10.1088\/1751-8121\/ac16c6","relation":{},"ISSN":["1751-8113","1751-8121"],"issn-type":[{"value":"1751-8113","type":"print"},{"value":"1751-8121","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,4]]},"assertion":[{"value":"Rare events for product fractal sets\n                      *","name":"article_title","label":"Article Title"},{"value":"Journal of Physics A: Mathematical and Theoretical","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2021 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2021-02-22","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-07-21","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-08-04","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}