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For each singular hyperbolic homoclinic class whose periodic orbits are all homoclinically related and such that the space of ergodic probability measures is connected, we prove that: (i) level sets associated to continuous observables are dense in the homoclinic class and satisfy a variational principle; (ii) irregular sets are either empty or are Baire generic and carry full topological entropy. The assumptions are satisfied by <jats:italic>C<\/jats:italic>\n                  <jats:sup>1<\/jats:sup>-generic singular hyperbolic attractors and <jats:italic>C<jats:sup>r<\/jats:sup>\n                  <\/jats:italic>-generic geometric Lorenz attractors <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mo stretchy=\"false\">(<\/mml:mo>\n                        <mml:mi>r<\/mml:mi>\n                        <mml:mo>\u2a7e<\/mml:mo>\n                        <mml:mn>2<\/mml:mn>\n                        <mml:mo stretchy=\"false\">)<\/mml:mo>\n                     <\/mml:math>\n                  \n                  <\/jats:inline-formula>. Finally we prove level-2 large deviations bounds for weak Gibbs measures, which provide a large deviations principle in the special case of Gibbs measures. The main technique we apply is the horseshoe approximation property.<\/jats:p>","DOI":"10.1088\/1361-6544\/ace491","type":"journal-article","created":{"date-parts":[[2023,8,29]],"date-time":"2023-08-29T02:15:07Z","timestamp":1693275307000},"page":"5216-5251","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["On multifractal analysis and large deviations of singular hyperbolic attractors"],"prefix":"10.1088","volume":"36","author":[{"given":"Yi","family":"Shi","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2142-4705","authenticated-orcid":true,"given":"Xueting","family":"Tian","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0902-8718","authenticated-orcid":true,"given":"Paulo","family":"Varandas","sequence":"additional","affiliation":[]},{"given":"Xiaodong","family":"Wang","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2023,8,29]]},"reference":[{"key":"nonace491bib1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11856-011-0041-5","type":"journal-article","article-title":"Nonuniform hyperbolicity for C 1-generic diffeomorphisms","volume":"183","author":"Abdenur","year":"2011","journal-title":"Israel J. 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