ERGODIC PROPERTIES OF A CLASS OF DISCRETE ABELIAN GROUP EXTENSIONS OF RANK-ONE TRANSFORMATIONS

作者：Dodd Chris^*; Jeasakul Phakawa; Jirapattanakul Anne; Kane Daniel M; Robinson Becky; Stein Noah D; Silva Cesar E

来源：Colloquium Mathematicum, 2010, 119(1): 1-22.

DOI：10.4064/cm119-1-1

• infinite measure-preserving
• ergodic
• group extensions
• multiple recurrence

We define a class of discrete Abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply recurrent. We then study conditions sufficient for showing that Cartesian products of transformations are conservative for a class of invertible infinite measure-preserving transformations and provide examples of these transformations.

• 出版日期2010