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

Chris Dodd; Phakawa Jeasakul; Anne Jirapattanakul; Daniel M. Kane; Becky Robinson; Noah D. Stein; Cesar E. Silva

doi:10.4064/cm119-1-1

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

Chris Dodd, Phakawa Jeasakul, Anne Jirapattanakul, Daniel M. Kane, Becky Robinson, Noah D. Stein, Cesar E. Silva

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	1-22
Number of pages	22
Journal	Colloquium Mathematicum
Volume	119
Issue number	1
DOIs	https://doi.org/10.4064/cm119-1-1
State	Published - 2010

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http://dx.doi.org/10.4064/cm119-1-1

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abstract = "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.",

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AU - Robinson, Becky

AU - Stein, Noah D.

AU - Silva, Cesar E.

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AB - 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.

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

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