攀援集与Furstenberg族

Scrambled Sets via Furstenberg Families

本文用Furstenberg族研究了弱混合系统的攀援集.证明了:对于每一个有不动点的离散弱混合系统(X,f)而言,存在一个不变的稠密的(τF_(inf),F_(inf))-攀援集;对于每一个弱混合的有任意周期的周期点的周期吸附系统(X,f)而言,存在一个不变的稠密的(τF_(inf),τF_(inf))-攀援集,其中τF_(inf)为非负整数集的全体thick集组成的集族,F_(inf)为非负整数集的全体无限子集组成的集族。

This article is devoted to dealing with scrambled sets via Furstenberg families.We show that every weakly mixing system(X,f) with a fixed point has an invariant and dense(τ F_(inf),F_(inf))-scrambled set,where f is a homeomorphism,τF_(inf) is the family of all thick sets of nonnegative integers and F_(inf) is the family of all infinite sets of nonnegative integers.Additionally,we prove that every weakly mixing periodically adsorbing system which contains n-period points for all positive integers n has an invariant and dense(τF_(inf),τF_(inf))-scrambled set.