For any minimal system(X,T)and d≥1,there is an associated minimal system(N_(d)(X),G_(d)(T)),where G_(d)(T)is the group generated by T x…x T andT xT^(2)x.…x T^(d),and N_(d)(X)is the orbit closure of the diagonal und...For any minimal system(X,T)and d≥1,there is an associated minimal system(N_(d)(X),G_(d)(T)),where G_(d)(T)is the group generated by T x…x T andT xT^(2)x.…x T^(d),and N_(d)(X)is the orbit closure of the diagonal under G_(d)(T).It is known that the maximal d-step pro-nilfactor of N_(d)(X)is N_(d)(Xa),where X_(d)is the maximal d-step pro-nilfactor of X.In this paper,we further study the structure of N_(d)(X).We show that the maximal distal factor of N_(d)(X)is N_(d)(X_(dis))with X_(dis)being the maximal distal factor of X,and prove that as minimal system(N_(d)(X),G_(d)(T))has the same structure theorem as(X,T).In addition,a non-saturated metric example(X,T)is constructed,which is not T x T^(2)-saturated and is a Toeplitz minimal system.展开更多
文摘For any minimal system(X,T)and d≥1,there is an associated minimal system(N_(d)(X),G_(d)(T)),where G_(d)(T)is the group generated by T x…x T andT xT^(2)x.…x T^(d),and N_(d)(X)is the orbit closure of the diagonal under G_(d)(T).It is known that the maximal d-step pro-nilfactor of N_(d)(X)is N_(d)(Xa),where X_(d)is the maximal d-step pro-nilfactor of X.In this paper,we further study the structure of N_(d)(X).We show that the maximal distal factor of N_(d)(X)is N_(d)(X_(dis))with X_(dis)being the maximal distal factor of X,and prove that as minimal system(N_(d)(X),G_(d)(T))has the same structure theorem as(X,T).In addition,a non-saturated metric example(X,T)is constructed,which is not T x T^(2)-saturated and is a Toeplitz minimal system.
