New York Journal of Mathematics
Volume 9 (2003) 1-22


Kate Gruher, Fred Hines, Deepam Patel, Cesar E. Silva and Robert Waelder

Power weak mixing does not imply multiple recurrence in infinite measure and other counterexamples

Published: January 23, 2003
Keywords: Multiple recurrence, power weak mixing, infinite measure-preserving, rank one staircases
Subject: Primary 37A40. Secondary 28D

We show that for infinite measure-preserving transformations, power weak mixing does not imply multiple recurrence. We also show that the infinite measure-preserving "Chacon transformation" known to have infinite ergodic index is not power weakly mixing, and is 3-recurrent but not multiply recurrent. We also construct some doubly ergodic infinite measure-preserving transformations that are not of positive type but have conservative Cartesian square. Finally, we study the power double ergodicity property.

Author information

Kate Gruher:
University of Chicago, Chicago, IL 60637, USA

Fred Hines:
Williams College, Williamstown, MA 01267, USA

Deepam Patel:
Brandeis University, Waltham, MA 02454, USA

Cesar E. Silva:
Department of Mathematics, Williams College, Williamstown, MA 01267, USA

Robert Waelder:
University of California, Berkeley, CA 94720, USA