Shadowing Property, Weak Mixing and Regular Recurrence
Shadowing Property, Weak Mixing and Regular Recurrence
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DOI：
10.1007/s10884-013-9338-x
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发表时间：
2013-11
影响因子：
1.3
通讯作者：
Jian Li;P. Oprocha
中科院分区：
文献类型：
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作者：
Jian Li;P. Oprocha
我们证明了具有阴影性质的非游荡动力系统是等连续的或具有正熵的，并且在这种情况下均匀的正熵等价于弱混合。我们还证明了弱混合和阴影性质意味着在跟踪中具有一种特殊规则的规范性质（周期规范性质的弱化版本）。这反过来意味着在正则循环点的轨道闭包上支持的遍历测度的集合在所有不变测度的空间中是密集的（特别是，在这样一个系统中的不变测度形成Poulsen单纯形，直到仿射同胚）。
We show that a non-wandering dynamical system with the shadowing property is either equicontinuous or has positive entropy and that in this context uniformly positive entropy is equivalent to weak mixing. We also show that weak mixing together with the shadowing property imply the specification property with a special kind of regularity in tracing (a weaker version of periodic specification property). This in turn implies that the set of ergodic measures supported on the closures of orbits of regularly recurrent points is dense in the space of all invariant measures (in particular, invariant measures in such a system form the Poulsen simplex, up to an affine homeomorphism).