Bessa, MárioVarandas, Paulo2023-05-292023-05-292010M. Bessa, P. Varandas, On the Entropy of Conservative Flows, Qualitative Theory of Dynamical Systems, 10, 1, 11-22, 2010http://hdl.handle.net/10400.2/13882We obtain a C1-generic subset of the incompressible flows in a closed three-dimensional manifold where Pesin’s entropy formula holds thus establishing the continuous-time version of Tahzibi (C R Acad Sci Paris I 335:1057–1062, 2002). Moreover, in any compact manifold of dimension larger or equal to three we obtain that the metric entropy function and the integrated upper Lyapunov exponent function are not continuous with respect to the C1 Whitney topology. Finally, we establish the C2- genericity of Pesin’s entropy formula in the context of Hamiltonian four-dimensional flows.engDivergence-free vector fieldsHamiltoniansLyapunov exponentsMetric entropyjournal article10.1007/s12346-010-0033-6