动力系统中n重回复时间集的性质研究

The Study of n Recurrent Set in Dynamical System

摘要: 设(X,G)是一个G-系统，其中X是紧致度量空间(度量为d)，G:X→X是连续映射。基于Furtenberg族，我们利用动力系统的复杂性和回复性，证明了对任意μ∈M(X,G)，存在一个μ(X₀)=1的Borel子集X₀，使得对任意x∈X，d∈ℕ以及x的任意邻域U，集合N_{T×T²×…×T^d}((x,x…,x),U₁×U₂×…×U_d)具有正上F-密度。

Abstract: Let (X,G) be a G-system, where X is the compact metric space (metric d) and G:X→X is a continuous map. Based on the Furtenberg family, we use the complexity and recurrence of the dynamical system to prove that for any μ∈M(X,G), there exists an Borel subset X₀ of μ(X₀)=1 such that for any x∈X，d∈ℕ and any neighborhood U of x, the set N_{T×T²×…×T^d}((x,x…,x),U₁×U₂×…×U_d) has a positive upper F-density.