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The convergence to the Gumbel law of observable recurrences gives information on the fractal structure of the image of the invariant measure by the observable. We provide illustrations on idealized and physical systems.<\/jats:p>","DOI":"10.1088\/1361-6544\/abaff1","type":"journal-article","created":{"date-parts":[[2020,11,12]],"date-time":"2020-11-12T09:35:18Z","timestamp":1605173718000},"page":"118-163","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Extreme value distributions of observation recurrences"],"prefix":"10.1088","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8960-7279","authenticated-orcid":false,"given":"Th","family":"Caby","sequence":"first","affiliation":[]},{"given":"D","family":"Faranda","sequence":"additional","affiliation":[]},{"given":"S","family":"Vaienti","sequence":"additional","affiliation":[]},{"given":"P","family":"Yiou","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2020,11,10]]},"reference":[{"key":"nonabaff1bib1","doi-asserted-by":"publisher","first-page":"8229","DOI":"10.1090\/s0002-9947-2014-06300-9","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. 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