發(fā)布時間：2018-10-14 10:35

【摘要】：設(shè)β1為實數(shù),T_β為[0,1]的β變換.攀援集的任何兩個點隨著時間的轉(zhuǎn)移會越來越接近但同時又總能在任意長時間后保持一定的距離.證明了在Lebesgue測度意義下關(guān)于T_β的攀援集是一個零測集.Distal點對的兩個點表示隨著時間的轉(zhuǎn)移始終保持著一定的距離.如果固定其中一個點x_0,所有滿足x∈[0,1)且lim inf n→∞|T_β~n(x)-T_β~n(x_0)|0的點稱為關(guān)于x_0的distal集,如果把這個集合記為R_β(x_0),根據(jù)Borel-Cantelli引理得到R_β(x_0)的Lebesgue測度為零.
[Abstract]:Let 尾 _ 1 be a real number and T _ 尾 be a 尾 -transformation of [0]. Any two points in the climbing set will get closer and closer over time, but at the same time they can keep a certain distance after any long time. It is proved that the climbing set of T _ 尾 in the sense of Lebesgue measure is a zero measure set, and that the two points of Distal point pair always keep a certain distance with the time transfer. If one of the points x0 is fixed, all the points satisfying x 鈭，

本文編號：2270193