逆极限空间的转移映射

The Shift Maps on the Inverse Limit Spaces

证明了关于X的逆极限空间的转移映射具有下列结论 :(1)若 f是连续满射 ,则f具有Korner性质的充要条件是转移映射具有Korner性质 ;(2 ) f在其测度中心上是Li_Yorke混沌的当且仅当转移映射在其测度中心上是Li_Yorke混沌的 ,对Devaney混沌也如此 .

Let X be a compact metric space and f:X→X be continuous.The following results about the shift maps on the inverse limit spaces are proved: (1) If f is onto ,then f possesses the Korner's property if and only if the shift map has the Korner's property; (2) The f is chaotic in the sense of Li_Yorke on its measure centre if and only if the shift map is chaotic in the sense of Li_Yorke on its measure centre. This also applies to the chaos in the sense of Devaney.