کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4659608 1344329 2011 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Transitive points via Furstenberg family
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Transitive points via Furstenberg family
چکیده انگلیسی

Let (X,T) be a topological dynamical system and F be a Furstenberg family (a collection of subsets of Z+ with hereditary upward property). A point x∈X is called an F-transitive one if {n∈Z+:Tnx∈U}∈F for every non-empty open subset U of X; the system (X,T) is called F-point transitive if there exists some F-transitive point. In this paper, we aim to classify transitive systems by F-point transitivity. Among other things, it is shown that (X,T) is a weakly mixing E-system (resp. weakly mixing M-system, HY-system) if and only if it is {D-sets}-point transitive (resp. {central sets}-point transitive, {weakly thick sets}-point transitive).It is shown that every weakly mixing system is Fip-point transitive, while we construct an Fip-point transitive system which is not weakly mixing. As applications, we show that every transitive system with dense small periodic sets is disjoint from every totally minimal system and a system is Δ⁎(Fwt)-transitive if and only if it is weakly disjoint from every P-system.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 158, Issue 16, 1 October 2011, Pages 2221-2231