关于超空间非自治动力系统分布混沌的研究

Research on Distributional Chaos in Hyperspace Non-Autonomous Systems

摘要: 本文主要研究超空间非自治动力系统分布混沌的一些性质。在强一致收敛的条件下，得到了序列映射是第二型分布混沌(DC2, DC2’)与极限映射是第二型分布混沌(DC2, DC2’)的关系。在一致收敛条件下，得到了超空间非自治动力系统的第二型分布混沌(DC2’)保持迭代不变性。最后，证明了超空间非自治动力系统中$\left(K\left(X\right),\overline{f_{1,\infty }}\right)$ 是Li-Yorke混沌或$\left(K\left(Y\right),\overline{g_{1,\infty }}\right)$ 是Li-Yorke混沌当且仅当$\left(K\left(X\right)\times K\left(Y\right),\overline{f_{1,\infty }}\times \overline{g_{1,\infty }}\right)$ 是Li-Yorke混沌。

Abstract: This paper mainly studies some properties of distributional chaos in hyperspace non-autonomous dynamical systems. Under the condition of strong uniform convergence, the relationship between the sequence mapping being the type 2 of distributional chaos (DC2, DC2’) and the limit mapping being the type 2 of distributional chaos (DC2, DC2’) was obtained. Under the condition of uniform convergence, the type 2 of distributional chaos (DC2’) of the hyperspace non-autonomous dynamical system maintains iterative invariance. Finally, it is proved that in a hyperspace non-autonomous dynamical system, that $\left(K\left(X\right),\overline{f_{1,\infty }}\right)$ is Li-Yorke chaos or that $\left(K\left(Y\right),\overline{g_{1,\infty }}\right)$ is Li-Yorke chaos if and only if that $\left(K\left(X\right)\times K\left(Y\right),\overline{f_{1,\infty }}\times \overline{g_{1,\infty }}\right)$ is Li-Yorke chaos.