A variation on the variational principle and applications to entropy pairs
A variation on the variational principle and applications to entropy pairs
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DOI：
10.1017/s0143385797069794
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发表时间：
1997-02
影响因子：
0.9
通讯作者：
F. Blanchard;E. Glasner;B. Host
中科院分区：
文献类型：
--
作者：
F. Blanchard;E. Glasner;B. Host
变分原理表明，一个拓扑动力系统的拓扑熵等于不变测度的熵的上确界。已证明对于任何有限开覆盖，存在一个不变测度，使得这个覆盖的拓扑熵小于或等于所有更细划分的熵。这个结果的一个推论是，对于任何具有正拓扑熵的动力系统，存在一个不变测度，其熵对的集合等于拓扑熵对的集合。
The variational principle states that the topological entropy of a topological dynamical system is equal to the sup of the entropies of invariant measures. It is proved that for any finite open cover there is an invariant measure such that the topological entropy of this cover is less than or equal to the entropies of all finer partitions. One consequence of this result is that for any dynamical system with positive topological entropy there exists an invariant measure whose set of entropy pairs is equal to the set of topological entropy pairs.