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Publication
On the entropy of conservative flows
Authors
Advisor(s)
Abstract(s)
We 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.
Description
Keywords
Divergence-free vector fields Hamiltonians Lyapunov exponents Metric entropy
Citation
M. Bessa, P. Varandas, On the Entropy of Conservative Flows, Qualitative Theory of Dynamical Systems, 10, 1, 11-22, 2010
Publisher
Springer