Please wait a minute...
北京大学期刊网 | 作者  审稿人  编委专家  工作人员

首页   |   关于   |   浏览   |   投稿指南   |   新闻公告
数学进展 - 2018, Vol. 47(2): 207-214
研究论文
半群作用的稠密小周期集系统与完全传递系统
Dense Small Periodic Sets and Total Transitivity of Semigroup Actions

汪火云1,朱桂芳1,吴红英2
WANG Huoyun1,*, ZHU Guifang1,**, WU Hongying2,***}

1. 广州大学数学与信息科学学院, 广州, 广东, 510006;
2. 怀化学院数学与计算科学学院, 怀化, 湖南, 418008
1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong, 510006, P. R. China;
2. School of Mathematics and Computing Science, Huaihua University, Huaihua, Hunan, 418008, P. R. China

收稿日期: 2016-09-25
出版日期: 2018-05-16
2018, Vol. 47(2): 207-214
DOI: 10.11845/sxjz.2016114b


PDF
[216 KB]
31
下载
181
浏览

引用导出
0
    /   /   推荐

摘要 称一个动力系统~$(S,X)$ 具有稠密g-小周期集, 如果对任意非空开集~$U\subset X$, 存在非空闭子集~$Y\subset U$ 和~$S$ 的一个g-syndetic 子半群~$T$, 使得~$TY\subset Y$; 称一个传递的动力系统~$(S,X)$ 是g-完全传递的, 如果对~$S$ 的每一个g-syndetic 子半群~$T$,~$(T,X)$ 都是传递的. 本文指出, 每一个具有稠密 g-小周期集的g-完全传递系统~$(S,X)$ 不交于任何极小系统, 其中~$S$ 是一个可数交换半群,~$S$ 最多只有可数个g-syndetic 子半群且~$S$ 中的每一个元~$S$都为$X$到自身的满射.
关键词 稠密g-小周期集g-完全传递g-syndetic子半群半群作用    
Abstract:A dynamical system $(S,X)$ is defined as a system with dense g-small periodic sets, if for every nonempty open subset $U$ of $X$ there exist a nonempty closed subset $Y$ of $U$ and a g-syndetic subsemigroup $T$ of $S$ such that $TY\subset Y$. A transitive dynamical system $(S,X)$ is called g-totally transitive, if $(T,X)$ is transitive for every g-syndetic subsemigroup $T$ of $S$. In this article, we point out that every g-totally transitive dynamical system $(S,X)$ with dense g-small periodic sets is disjoint from all minimal systems, where $S$ is a countable abelian semigroup, $S$ has at most countably many g-syndetic subsemigroups and every $s$ of $S$ is a surjective map from $X$ onto itself.
Key wordsdense g-small periodic sets    g-total transitivity    g-syndetic subsemigroup    semigroup actions
PACS:  O189.11  
[1] Akin, E., Recurrence in Topological Dynamics: Furstenberg Families and Ellis Actions, New York: Plenum Press, 1997.
[2] Bergelson, V., Hindman, N. and McCutcheon, R., Notions of size and combinatorial properties of quotient sets in semigroups, Topology Proc., 1998, 23: 23-60.
[3] Ellis, D.B., Ellis, R. and Nerurkar, M., The topological dynamics of semigroup actions, Trans. Amer. Math. Soc., 2001, 353(4): 1279-1320.
[4] Furstenberg, H., Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton: Princeton Univ. Press, 1981.
[5] Gottschalk, W. and Hedlund, G., Topological Dynamics, Providence, RI: AMS, 1955.
[6] Hindman, N. and Strauss, D., Algebra in the Stone-Cech Compactification: Theory and Applications, Berlin: Walter de Gruyter, 1998.
[7] Huang, W. and Ye, X.D., Dynamical systems disjoint from any minimal system, Trans. Amer. Math. Soc., 2005, 357(2): 669-694.
[8] Kontorovich, E. and Megrelishvili, M., A note on sensitivity of semigroup actions, Semigroup Forum, 2008, 76(1): 133-141.
[9] Li, J., Transitive points via Furstenberg family, Topol. Appl., 2011, 158(16): 2221-2231.
[10] Miller, A., Envelopes of syndetic subsemigroups of the acting topological semigroup in a semiflow, Topol. Appl., 2011, 158(3): 291-297.
[11] Oprocha, P. and Zhang, G.H., On weak product recurrence and synchronization of return times, Adv. Math., 2013, 244: 395-412.
[12] Schneider, F.M., Kerkhoff, S., Behrisch, M. and Siegmund, S., Chaotic actions of topological semigroups, Semigroup Forum, 2013, 87(3): 590-598.
[13] Wang, H.Y., Zhu, G.F., Tang, Y. and Huang, L., Some dynamical properties of syndetic subsemigroups actions, J. Dyn. Control Syst., 2015, 21(1): 147-154.
[1] 王汉锋,贺伟. 具有代数结构的拓扑空间[J]. 数学进展, 2017, 46(5): 735-742.
[2] 朴勇杰. 锥度量空间上满足新的Lipschitz条件的三个映射的公共不动点[J]. 数学进展, 2017, 46(1): 122-132.
[3] 朴勇杰. 复值度量空间上满足分式收缩条件的映射族的唯一公共不动点[J]. 数学进展, 2016, 45(4): 581-588.
[4] 林寿, 林福财. 一个正规的Moore仿拓扑群[J]. 数学进展, 2016, 45(1): 153-158.
[5] 唐忠宝, 林福财. 统计版本的序列空间和Fr\'{e}chet-Urysohn空间[J]. 数学进展, 2015, 44(6): 945-954.
[6] 凌学炜, 林寿. 关于度量空间的开几乎$s$映像[J]. 数学进展, 2019, 48(4): 489-496.
Viewed
Full text


Abstract

Cited

  Discussed   
首页 · 关于 · 关于OA · 法律公告 · 收录须知 · 联系我们 · 注册 · 登录


© 2015-2017 北京大学图书馆 .