论文标题
与非周期点的非零熵的封闭关系
Closed relations with non-zero entropy that generate no periodic points
论文作者
论文摘要
该论文是由E. Akin的有关动态系统和封闭关系[A]的书以及J. Kennedy's和G. Erceg最近关于封闭间隔的封闭关系的熵的论文[EK]。在目前的论文中，我们在任何紧凑的度量空间X上介绍了封闭关系g的熵，并显示其基本特性。当这样的关系G产生周期点或有限地生成Cantor集时，我们还会介绍。然后，我们表明，周期性生成的综合点，Mahavier产品和封闭关系的熵由拓扑结合保留。除其他外，这概括了有关连续映射的拓扑结合的众所周知的结果。最后，我们证明了一个定理，为[0,1]上的闭合关系G提供了足够的条件，使其具有非零熵。然后，我们提出了[0,1]上闭合关系g的各种示例，因此（1）g的熵为非零，（2）G。没有g生成周期点或完全周期点，并且（3）G。
The paper is motivated by E. Akin's book about dynamical systems and closed relations [A], and by J. Kennedy's and G. Erceg's recent paper about the entropy of closed relations on closed intervals [EK]. In present paper, we introduce the entropy of a closed relation G on any compact metric space X and show its basic properties. We also introduce when such a relation G generates a periodic point or finitely generates a Cantor set. Then we show that periodic points, finitely generated Cantor sets, Mahavier products and the entropy of closed relations are preserved by topological conjugations. Among other things, this generalizes the well-known results about the topological conjugacy of continuous mappings. Finally, we prove a theorem, giving sufficient conditions for a closed relation G on [0,1] to have a non-zero entropy. Then we present various examples of closed relations G on [0,1] such that (1) the entropy of G is non-zero, (2) no periodic point or exactly one periodic point is generated by G, and (3) no Cantor set is finitely generated by G.
