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Let $$\\mathfrak {X}^{0,1}_{\\nu ,\\ell }(M)\\subset \\mathfrak {X}^{0,1}_\\nu (M)$$<\/jats:tex-math>\n \n \n \n X<\/mml:mi>\n <\/mml:mrow>\n \n \u03bd<\/mml:mi>\n ,<\/mml:mo>\n \u2113<\/mml:mi>\n <\/mml:mrow>\n \n 0<\/mml:mn>\n ,<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msubsup>\n \n (<\/mml:mo>\n M<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n \u2282<\/mml:mo>\n \n \n X<\/mml:mi>\n <\/mml:mrow>\n \u03bd<\/mml:mi>\n \n 0<\/mml:mn>\n ,<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msubsup>\n \n (<\/mml:mo>\n M<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> be the subset of vector fields satisfying the $$\\ell $$<\/jats:tex-math>\n \u2113<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-property, a property that implies $$C^1$$<\/jats:tex-math>\n \n C<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-regularity $$\\nu $$<\/jats:tex-math>\n \u03bd<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-almost everywhere. We prove that there exists a residual subset \"Equation missing\" with respect to $$\\Vert \\,{\\cdot }\\,\\Vert _{0,1}$$<\/jats:tex-math>\n \n \n \u2016<\/mml:mo>\n \n \u00b7<\/mml:mo>\n \n \u2016<\/mml:mo>\n <\/mml:mrow>\n \n 0<\/mml:mn>\n ,<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> such that Pesin\u2019s entropy formula holds, i.e. for any \"Equation missing\" the metric entropy equals the integral, with respect to $$\\nu $$<\/jats:tex-math>\n \u03bd<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, of the sum of the positive Lyapunov exponents.<\/jats:p>","DOI":"10.1007\/s40879-023-00611-6","type":"journal-article","created":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T02:28:57Z","timestamp":1679884137000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Lyapunov exponents and entropy for divergence-free Lipschitz vector fields"],"prefix":"10.1007","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1758-2225","authenticated-orcid":false,"given":"M\u00e1rio","family":"Bessa","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,3,20]]},"reference":[{"key":"611_CR1","unstructured":"Abramov, L.M.: On the entropy of a flow. 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