{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T02:00:00Z","timestamp":1769133600992,"version":"3.49.0"},"reference-count":28,"publisher":"IOP Publishing","issue":"1","license":[{"start":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T00:00:00Z","timestamp":1769040000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T00:00:00Z","timestamp":1769040000000},"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":["2022.07167.PTDC"],"award-info":[{"award-number":["2022.07167.PTDC"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2026,1,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msup>\n                            <mml:mrow>\n                              <mml:mrow>\n                                <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:mrow>\n                            <mml:mi>d<\/mml:mi>\n                          <\/mml:msup>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -valued observables evaluated along the orbits of the systems. We study this cross-sectional dependence, which results from the combination of a spatial and a temporal dependence structures. We give several illustrative applications, where concrete systems and dependence sources are introduced and analysed.\n                  <\/jats:p>","DOI":"10.1088\/1361-6544\/ae36db","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T09:38:06Z","timestamp":1769074686000},"page":"015023","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Multivariate extreme values for dynamical systems"],"prefix":"10.1088","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5114-4421","authenticated-orcid":true,"given":"Romain","family":"Aimino","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7307-3441","authenticated-orcid":false,"given":"Ana","family":"Cristina Moreira Freitas","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0868-2654","authenticated-orcid":true,"given":"Jorge","family":"Milhazes Freitas","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0042-0713","authenticated-orcid":true,"given":"Mike","family":"Todd","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2026,1,22]]},"reference":[{"key":"nonae36dbbib1","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":"nonae36dbbib2","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":"nonae36dbbib3","doi-asserted-by":"crossref","DOI":"10.1002\/0470012382","type":"book","article-title":"Statistics of extremes","author":"Beirlant","year":"2004"},{"key":"nonae36dbbib4","doi-asserted-by":"publisher","first-page":"e2782","DOI":"10.1002\/env.2782","type":"journal-article","article-title":"Stable sums to infer high return levels of multivariate rainfall time series","volume":"34","author":"Buritic\u00e1","year":"2023","journal-title":"Environmetrics"},{"key":"nonae36dbbib5","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1080\/14689367.2015.1056722","type":"journal-article","article-title":"Extremal dichotomy for uniformly hyperbolic systems","volume":"30","author":"Carvalho","year":"2015","journal-title":"Dyn. Syst."},{"key":"nonae36dbbib6","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2023.133968","type":"journal-article","article-title":"Cluster distributions for dynamically defined point processes","volume":"457","author":"Correia","year":"2024","journal-title":"Physica D"},{"key":"nonae36dbbib7","doi-asserted-by":"publisher","first-page":"835","DOI":"10.2307\/1427679","type":"journal-article","article-title":"Calculating the extremal index for a class of stationary sequences","volume":"23","author":"Chernick","year":"1991","journal-title":"Adv. in Appl. Probab."},{"key":"nonae36dbbib8","doi-asserted-by":"publisher","first-page":"2131","DOI":"10.4171\/jems\/808","type":"journal-article","article-title":"Convergence of marked point processes of excesses for dynamical systems","volume":"20","author":"Freitas","year":"2018","journal-title":"J. Eur. Math. Soc. (JEMS)"},{"key":"nonae36dbbib9","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1090\/tran\/7922","type":"journal-article","article-title":"Complete convergence and records for dynamically generated stochastic processes","volume":"373","author":"Freitas","year":"2020","journal-title":"Trans. Am. Math. Soc."},{"key":"nonae36dbbib10","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":"nonae36dbbib11","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1088\/1751-8121\/ac16c6","type":"journal-article","article-title":"Rare events for product fractal sets","volume":"54","author":"Freitas","year":"2021","journal-title":"J. Phys.A"},{"key":"nonae36dbbib12","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":"nonae36dbbib13","doi-asserted-by":"publisher","first-page":"1653","DOI":"10.1016\/j.spa.2014.11.011","type":"journal-article","article-title":"Speed of convergence for laws of rare events and escape rates","volume":"125","author":"Freitas","year":"2015","journal-title":"Stochastic Process. Appl."},{"key":"nonae36dbbib14","type":"journal-article","article-title":"Enriched functional limit theorems for dynamical systems","author":"Freitas","year":"2025","journal-title":"Annali della Scuola Normale Superiore di Pisa. Classe di Scienze."},{"key":"nonae36dbbib15","author":"Falk","year":"2011","edition":"extended edn","type":"book"},{"key":"nonae36dbbib16","doi-asserted-by":"publisher","DOI":"10.1088\/1748-9326\/acbc37","type":"journal-article","article-title":"Persistent anticyclonic conditions and climate change exacerbated the exceptional 2022 European-mediterranean drought","volume":"18","author":"Faranda","year":"2023","journal-title":"Environ. Res. Lett."},{"key":"nonae36dbbib17","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1080\/14689367.2013.806731","type":"journal-article","article-title":"Extremal behaviour of chaotic dynamics","volume":"28","author":"Freitas","year":"2013","journal-title":"Dyn. Syst."},{"key":"nonae36dbbib18","doi-asserted-by":"publisher","DOI":"10.1063\/1.5027386","type":"journal-article","article-title":"Correlation dimension and phase space contraction via extreme value theory","volume":"28","author":"Faranda","year":"2018","journal-title":"Chaos"},{"key":"nonae36dbbib19","doi-asserted-by":"publisher","first-page":"1363","DOI":"10.1017\/S014338571000057X","type":"journal-article","article-title":"Extreme value theory and return time statistics for dispersing billiard maps and flows, Lozi maps and Lorenz-like maps","volume":"31","author":"Gupta","year":"2011","journal-title":"Ergodic Theory Dynam. Systems"},{"key":"nonae36dbbib20","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/0047-259X(89)90028-6","type":"journal-article","article-title":"Extreme value theory for multivariate stationary sequences","volume":"29","author":"Hsing","year":"1989","journal-title":"J. Multivariate Anal."},{"key":"nonae36dbbib21","first-page":"234","type":"book","volume":"vol 51","author":"H\u00fcsler","year":"1989"},{"key":"nonae36dbbib22","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/s00220-020-03795-0","type":"journal-article","article-title":"Limiting entry and return times distribution for arbitrary null sets","volume":"378","author":"Haydn","year":"2020","journal-title":"Commun. Math. Phys."},{"key":"nonae36dbbib23","doi-asserted-by":"crossref","DOI":"10.1002\/9781118632321","type":"book","article-title":"Extremes and recurrence in dynamical systems","author":"Lucarini","year":"2016"},{"key":"nonae36dbbib24","author":"Leadbetter","year":"1983","type":"book"},{"key":"nonae36dbbib25","doi-asserted-by":"publisher","DOI":"10.1029\/2022GL101008","type":"journal-article","article-title":"On the systematic occurrence of compound cold spells in north America and wet or windy extremes in Europe","volume":"50","author":"Messori","year":"2023","journal-title":"Geophys. Res. Lett."},{"key":"nonae36dbbib26","doi-asserted-by":"publisher","first-page":"543","DOI":"10.6028\/jres.099.052","type":"journal-article","article-title":"On the multivariate extremal index","volume":"99","author":"Nandagopalan","year":"1994","journal-title":"J. Res. Nat. Inst. Stand. Technol."},{"key":"nonae36dbbib27","doi-asserted-by":"publisher","first-page":"138","DOI":"10.2307\/1427864","type":"journal-article","article-title":"Extreme value theory for a class of Markov chains with values in Rd","volume":"29","author":"Perfekt","year":"1997","journal-title":"Adv. Appl. Probab."},{"key":"nonae36dbbib28","first-page":"61","type":"journal-article","article-title":"Max-stable models for multivariate extremes","volume":"10","author":"Segers","year":"2012","journal-title":"REVSTAT"}],"container-title":["Nonlinearity"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ae36db","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ae36db\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ae36db\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ae36db\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T09:38:12Z","timestamp":1769074692000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ae36db"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,22]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,22]]},"published-print":{"date-parts":[[2026,1,30]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6544\/ae36db","relation":{},"ISSN":["0951-7715","1361-6544"],"issn-type":[{"value":"0951-7715","type":"print"},{"value":"1361-6544","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,22]]},"assertion":[{"value":"Multivariate extreme values for dynamical systems","name":"article_title","label":"Article Title"},{"value":"Nonlinearity","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2026 The Author(s). Published by IOP Publishing Ltd and the London Mathematical Society.","name":"copyright_information","label":"Copyright Information"},{"value":"2025-01-18","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-01-12","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-01-22","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}