一致空间上连续变换的拓扑熵及其计算

研究一致空间上连续变换的拓扑熵的性质和紧一致空间上扩张同胚拓扑熵的计算问题，证明Ｂｏｗｅｎ给出的度量空间的连续变换的拓 熵由其度量诱导的一致结构决定；对于可一致化的紧拓扑空间上的连续变换Ａｄｌｅｒ、Ｋｏｎｈｅｉｍ、ＭｃＡｎｄｒｅｗ及Ｂｏｗｅｎ定义的拓扑熵相同；变换是扩张变换等价于其有生成子；紧一致空间上扩张同胚的拓扑熵由其生成了或扩张常数决定。

Topological entropy of continuousformations on uniform spaces and its computation

The pmperties of the topological entropies of continuous transformations in uriform spaces and the calculating pmblem of the topological entropies of expansive homeomorphisms in compact uniform spaces is considered, It is shown that, (I) The Bowen' s topological entropy (TE) defined for uniformly continuous transformations in metric space is decided by the unform structure induced by the metric;(ii) AII Tes defined by Adler, Konheim, and McAndrew & Bowen, for continuous maps in unifomrzable compact space coincide with each other;(iii)A map is expansive homeomorphism if and only if it has a generator;(iv) The TE of an expansive homeomorphism in compact uniform space is decided by its generator or expansive constant.