Non-uniformly expanding dynamical systems: multi-dimension
Non-uniformly expanding dynamical systems: multi-dimension
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非均匀膨胀动力系统：多维
DOI：
10.3934/dcds.2019106
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Yuan-Ling Ye
中科院分区：
文献类型：
--
作者：
Yuan-Ling Ye
满足Thaler条件的区间[0，1]上的动力系统已被广泛研究。本文研究了R^d$（$d ≥ 1$）上非一致膨胀动力系统的不变密度和统计性质。本文提出了一个临界正则条件，它是对Thaler条件的补充和发展，并且与Lamperti准则有着密切的联系。在这种新的条件下，我们提供了一种研究动力系统的方法。给出了不变密度的连续性描述，建立了Perron-Frobenius迭代的收敛性定理. operator.is此外，我们建立了一个更准确的结果为一维。系统。
Dynamical systems on the interval [0, 1], satisfying the Thaler’s.condition, have been extensively studied. In this paper we consider invariant.density and statistical properties of non-uniformly expanding dynamical systems.on $R^d$ ($d ≥ 1$). We present a critical regular condition that is a supplement.and a development of the Thaler’s condition, and it is very closely related to.Lamperti’s criterion. Under this new condition, we offer a method for studying.the dynamical systems. A continuity description of the invariant density is presented;.and a convergence theorem for iterations of Perron-Frobenius operator.is set up. Furthermore, we establish a more exact result for one-dimensional.systems..