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期刊论文

DYNAMICAL SYSTEMS DISJOINT FROM ANY MINIMAL SYSTEM

黄文WEN HUANG AND XIANGDONG YE

AMERICAN MATHEMATICAL SOCIETY Volume 357, Number 2, Pages 669-694,-0001,():

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摘要/描述

Furstenberg showed that if two topological systems (X; T) and (Y; S) are disjoint, then one of them, say (Y; S), is minimal. When (Y; S) is nontrivial, we prove that (X; T) must have dense recurrent points, and there are countably many maximal transitive subsystems of (X; T) such that their union is dense and each of them is disjoint from (Y; S). Showing that a weakly mixing system with dense periodic points is in M, the collection of all systems disjoint from any minimal system, Furstenberg asked the question to characterize the systems in M. We show that a weakly mixing system with dense regular minimal points is in M, and each system in M has dense minimal points and it is weakly mixing if it is transitive. Transitive systems in M and having no periodic points are constructed. Moreover, we show thatthere is a distal system in M.

【免责声明】以下全部内容由[黄文]上传于[2005年05月13日 22时39分40秒],版权归原创者所有。本文仅代表作者本人观点,与本网站无关。本网站对文中陈述、观点判断保持中立,不对所包含内容的准确性、可靠性或完整性提供任何明示或暗示的保证。请读者仅作参考,并请自行承担全部责任。

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