Ergodicity and conservativity of products of infinite transformations and their inverses

Julien Clancy, et al. "Ergodicity and conservativity of products of infinite transformations and their inverses." Colloquium Mathematicae 143.2 (2016): 271-291. <http://eudml.org/doc/284016>.

@article{JulienClancy2016,
abstract = {We construct a class of rank-one infinite measure-preserving transformations such that for each transformation T in the class, the cartesian product T × T is ergodic, but the product $T × T^\{-1\}$ is not. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.},
author = {Julien Clancy, Rina Friedberg, Indraneel Kasmalkar, Isaac Loh, Tudor Pădurariu, Cesar E. Silva, Sahana Vasudevan},
journal = {Colloquium Mathematicae},
keywords = {infinite measure-preserving; ergodic; conservative; inverse transformation; rank-one},
language = {eng},
number = {2},
pages = {271-291},
title = {Ergodicity and conservativity of products of infinite transformations and their inverses},
url = {http://eudml.org/doc/284016},
volume = {143},
year = {2016},
}

TY - JOUR
AU - Julien Clancy
AU - Rina Friedberg
AU - Indraneel Kasmalkar
AU - Isaac Loh
AU - Tudor Pădurariu
AU - Cesar E. Silva
AU - Sahana Vasudevan
TI - Ergodicity and conservativity of products of infinite transformations and their inverses
JO - Colloquium Mathematicae
PY - 2016
VL - 143
IS - 2
SP - 271
EP - 291
AB - We construct a class of rank-one infinite measure-preserving transformations such that for each transformation T in the class, the cartesian product T × T is ergodic, but the product $T × T^{-1}$ is not. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.
LA - eng
KW - infinite measure-preserving; ergodic; conservative; inverse transformation; rank-one
UR - http://eudml.org/doc/284016
ER -