加权空间中一阶格点系统的统计解及其 Kolmogorov 熵

Abstract

Abstract:

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.

Key words: Lattice systems, Pullback attractor, Weighted spaces, Statistical solution, Kolmogorov entropy

CLC Number:

O175.8

Zou Tianfang,Zhao Caidi. Statistical Solutions and Kolmogorov Entropy for First-Order Lattice Systems in Weighted Spaces[J].Acta mathematica scientia,Series A, 2023, 43(5): 1559-1574.

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References 40

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

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