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首页> 外文期刊>Applied mathematics letters >Mixing properties for nonautonomous linear dynamics and invariant sets
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Mixing properties for nonautonomous linear dynamics and invariant sets

机译：非自治线性动力学和不变集的混合性质

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摘要

We study mixing properties (topological mixing and weak mixing of arbitrary order) for nonautonomous linear dynamical systems that are induced by the corresponding dynamics on certain invariant sets. The kinds of nonautonomous systems considered here can be defined using a sequence (T _i)i∈N of linear operators T _i:X→X on a topological vector space X such that there is an invariant set Y for which the dynamics restricted to Y satisfies a certain mixing property. We then obtain the corresponding mixing property on the closed linear span of Y. We also prove that the class of nonautonomous linear dynamical systems that are weakly mixing of order n contains strictly the corresponding class with the weak mixing property of order n+1.
机译：我们研究非自治线性动力系统的混合特性（拓扑混合和任意阶的弱混合），该线性系统由某些不变集上的相应动力学引起。此处考虑的非自治系统的类型可以使用拓扑向量空间X上的线性算子T _i：X→X的序列（T _i）i∈N来定义，这样就存在不变集Y，其动力学限于Y满足一定的混合性能。然后，我们在Y的闭合线性跨度上获得了相应的混合特性。我们还证明了，弱混合n阶的非自治线性动力系统的类别严格包含n + 1阶弱混合性质的相应类别。

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