论文标题
均匀空间上非自主动力系统的拓扑熵
Topological entropy of nonautonomous dynamical systems on uniform spaces
论文作者
论文摘要
在本文中，我们重点介绍了非自主动力系统$（x，f_ {0，\ infty}）$的一些属性，计算和估计，该属性是由连续自动映射$ f_ {0，\ infty} = \ {f_n \} n = 0} $ n = 0} $ n = $ n = $ n = $ n = $ n = $ n = $ n = $ n = $ n = $ n = $ n =我们获得了$（x，f_ {0，\ infty}）$，其$ k $ th产品系统和其$ n $ th迭代系统之间的拓扑熵关系。我们确认，$（x，f_ {0，\ infty}）$等于$ f_ {0，\ infty} $的熵限制为其非随机是其非随机设置的集合，前提是$ f_ {0，\ infty} $是equi-equi-nouble。我们证明$（x，f_ {0，\ infty}）$的熵小于或等于其极限系统$（x，f）$时，当$ f_ {0，\ infty} $均匀收敛到$ f $。我们表明，如果等极性缀合性是有限的，则两个拓扑等电压轭系统具有相同的熵。最后，我们得出了与过渡矩阵相关的耦合扩展系统的不变子系统的熵和下限的估计。
In this paper, we focus on some properties, calculations and estimations of topological entropy for a nonautonomous dynamical system $(X,f_{0,\infty})$ generated by a sequence of continuous self-maps $f_{0,\infty}=\{f_n\}_{n=0}^{\infty}$ on a compact uniform space $X$. We obtain the relations of topological entropy among $(X, f_{0,\infty})$, its $k$-th product system and its $n$-th iteration system. We confirm that the entropy of $(X, f_{0,\infty})$ equals to that of $f_{0,\infty}$ restricted to its non-wandering set provided that $f_{0,\infty}$ is equi-continuous. We prove that the entropy of $(X, f_{0,\infty})$ is less than or equal to that of its limit system $(X, f)$ when $f_{0,\infty}$ converges uniformly to $f$. We show that two topologically equi-semiconjugate systems have the same entropy if the equi-semiconjugacy is finite-to-one. Finally, we derive the estimations of upper and lower bounds of entropy for an invariant subsystem of a coupled-expanding system associated with a transition matrix.
