β-变换下攀援集和distal集的测度性质
发布时间：2018-10-14 10:35
【摘要】：设β1为实数,T_β为[0,1]的β变换.攀援集的任何两个点随着时间的转移会越来越接近但同时又总能在任意长时间后保持一定的距离.证明了在Lebesgue测度意义下关于T_β的攀援集是一个零测集.Distal点对的两个点表示随着时间的转移始终保持着一定的距离.如果固定其中一个点x_0,所有满足x∈[0,1)且lim inf n→∞|T_β~n(x)-T_β~n(x_0)|0的点称为关于x_0的distal集,如果把这个集合记为R_β(x_0),根据Borel-Cantelli引理得到R_β(x_0)的Lebesgue测度为零.
[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，
本文编号：2270193
[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，
本文编号：2270193
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