A note on Poincare recurrence for semigroup actions via Furstenberg family

作者：Tozatti Helio V M; Souza Josiney A^*

来源：Semigroup Forum, 2017, 94(1): 181-188.

DOI：10.1007/s00233-016-9828-3

• Recurrence
• Recursiveness
• Poisson stability
• Nonwandering point
• Furstenberg family

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 Poincar, 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.

• 出版日期2017-2