Ergodic properties of a class of discrete Abelian group extensions of rank-one transformations

Chris Dodd¹ ; Phakawa Jeasakul² ; Anne Jirapattanakul³ ; Daniel M. Kane⁴ ; Becky Robinson⁵ ; Noah D. Stein⁶ ; Cesar E. Silva⁷

¹ Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139, U.S.A.
² Economics Department University of California Berkeley, CA 94720, U.S.A.
³ 1022 International Affairs Building Columbia University 420 West 118th Street New York, NY 10027, U.S.A.
⁴ Department of Mathematics Harvard University Cambridge, MA 02138, U.S.A.
⁵ Williams College Williamstown, MA 01267, U.S.A.
⁶ Laboratory for Information and Decision Systems Massachusetts Institute of Technology Cambridge, MA 02139, U.S.A.
⁷ Department of Mathematics Williams College Williamstown, MA 01267, U.S.A.

Colloquium Mathematicum, Tome 119 (2010) no. 1, pp. 1-22

Résumé

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.

Détail

DOI : 10.4064/cm119-1-1

Keywords: define class discrete abelian group extensions rank one transformations establish necessary sufficient conditions these extensions power weakly mixing members class multiply recurrent study conditions sufficient showing cartesian products transformations conservative class invertible infinite measure preserving transformations provide examples these transformations