Cantor集合上的连续自映射

Continuous Maps on the Cantor Set

中文关键词:  Cantor集  连续自映射  有限型子移位  拓扑传递  拓扑混合．

英文关键词:Cantor set  continuous map  subshift of finite type  topologically transitivetopologically mixing.

中文摘要:

      本文证明了Ｃａｎｔｏｒ集Ｃ上所有拓扑共轭于（单边的）有限型子移位的连续自映射的集合在H中稠密，此外Ｃ上每个拓扑传递（混合）映射均可被拓扑共轭于有限型子移位的拓仆传递（混合）映射一致逼近．

英文摘要:

      In this paper we show that the set of all the continuous maps which are toplogi-cally conjugate to subshift of finite type is dense in the space of all the continuos mapsof the Cantor set with the topology of uniform convergence,Moreover,a topologically transitive(resp. mixing)map of the cantor set is approximated uniformly by topolgically transitive(resp.mixing)map which is topologically conjugate to subshift of finite type.