Bessa, Mário2023-05-312023-05-312023Bessa, M. Lyapunov exponents and entropy for divergence-free Lipschitz vector fields. European Journal of Mathematics 9, 20 (2023)http://hdl.handle.net/10400.2/13927Let X^0,1( M ) be the subset of divergence-free Lipschitz vector fields defined on a closed Riemannian manifold M endowed with the Lipschitz topology ∥ · ∥_0,1 where ν is the volume measure. Let L be the subset of vector fields satisfying the L-property, a property that implies C^1-regularity ν-almost everywhere. We prove that there exists a residual subset R ⊂ L with respect to ∥·∥0,1 such that Pesin’s entropy formula holds, i.e. for any X ∈ R the metric entropy equals the integral, with respect to ν, of the sum of the positive Lyapunov exponents.engVolume-preserving flowsLyapunov exponentsMetric entropyLipschitz vector fieldsjournal article10.1007/s40879-023-00611-6