加权空间中一阶格点系统的统计解及其Kolmogorov熵

Statistical Solutions and Kolmogorov Entropy for First-Order Lattice Systems in Weighted Spaces

该文研究加权空间中一阶格点系统的统计解及其Kolmogorov熵.文章首先证明一阶格点系统的初值问题在加权空间中具有整体适定性,且解映射生成一个连续过程并存在一族不变Borel概率测度,接着证明该族不变测度满足Liouville定理,且是该格点系统的统计解,最后给出了统计解的Kolmogorov熵的估计.

This article studies the statistical solution and Kolmogorov entropy for first-order lattice systems in weighted spaces.The authors first establish that the initial value problem is global well-posed in weighted spaces and that the continuous process associated to the solution operators possesses a family of invariant Borel probability measures.Then they prove that this family of invariant Borel probability measures meets the Liouville theorem and is a statistical solution of the addressed systems.Finally,they prove the upper bound of the Kolmogorov entropy of the statistical solution.