映射的拓朴熵密度及其性质

On Topological Entropy Density of Maps and its Property

在度量空间上,对于拓朴熵为无穷大的映射补充定义拓朴熵密度.相应地,得到拓朴熵密度密度的几个计算方法.同时,对于逆图象拓朴熵无穷大的映射,补充定义逆图象拓朴熵密度,一些已知的拓朴熵为无穷大拓朴熵无穷大的映射,可以给出有限的拓朴熵密度.

For a map of compact metric space, topological entropy density is defined for infinite topological entropy. Accordingly, the formulation of topological entropy dersity is gained. The inverse image entropy density is defined for infinite inverse image topologicalentropy, the formulation of topological entropy density is also gained for inverse image topological entropy density. Some known results are corollary of our works. This method opens a door to study two maps with infinite topological entropy but with finite topological entropy densities.