关于保守流的熵
On the entropy of conservative flows
摘要：
我们得到一个$C^1$ -通用子集的不可压缩流在一个封闭的三维流形，其中Pesin的熵公式成立，从而建立连续时间版本的\cite{T}。此外，在维数大于或等于3的紧致流形中，我们得到了度量熵函数和积分上李雅普诺夫指数函数关于$C^1$ Whitney拓扑是不连续的.最后，我们建立了$C^2$ -普适的Pesin的熵公式的上下文中的哈密顿四维流。
英文摘要：
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 \cite{T}. 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.
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