Qualitative Theory of Dynamical Systems

, Volume 10, Issue 1, pp 11–22 | Cite as

On the Entropy of Conservative Flows

  • Mário BessaEmail author
  • Paulo Varandas


We obtain a C 1-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 C 1 Whitney topology. Finally, we establish the C 2-genericity of Pesin’s entropy formula in the context of Hamiltonian four-dimensional flows.


Divergence-free vector fields Hamiltonians Lyapunov exponents Metric entropy 

Mathematics Subject Classification (2000)

Primary 37D30 37A35 Secondary 37C20 34D08 


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Authors and Affiliations

  1. 1.Centro de Matemática da Universidade do PortoPortoPortugal
  2. 2.ESTGOH-Instituto Politécnico de CoimbraOliveira do HospitalPortugal
  3. 3.Departamento de MatemáticaUniversidade Federal da BahiaSalvadorBrazil

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