A note on Poincaré recurrence for semigroup actions via Furstenberg family

详细信息    查看全文

• 作者：Hélio V. M. Tozatti ; Josiney A. Souza
• 关键词：Recurrence ; Recursiveness ; Poisson stability ; Nonwandering point ; Furstenberg family
• 刊名：Semigroup Forum
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：94
• 期：1
• 页码：181-188
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra;
• 出版者：Springer US
• ISSN：1432-2137
• 卷排序：94

文摘

This paper presents an explanation of recurrence for semigroup actions from two points of view. The first one considers the concept of recurrence in the Poincaré sense as stated in Souza (Semigroup Forum 83:351–370, 2011) while the second one considers the notion of recurrence via a Fursternberg family as defined in Akin (Recurrence in Topological Dynamics. Furstenberg and Ellis Action. Plenum Press, New York, 1997). A relationship between these notions of recurrence is presented.