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arXiv · 1408.2445

Ergodicity and Conservativity of products of infinite transformations and their inverses

Julien Clancy·Rina Friedberg·Indraneel Kasmalkar·Isaac Loh·Tudor Pădurariu·Cesar E. Silva·Sahana Vasudevan
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Abstract

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\times T$ of the transformation with itself is ergodic, but the product $T\times T^{-1}$ of the transformation with its inverse is not ergodic. 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.

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Julien Clancy, Rina Friedberg, Indraneel Kasmalkar, Isaac Loh, Tudor Pădurariu, Cesar E. Silva, Sahana Vasudevan. 2014-08-11. Ergodicity and Conservativity of products of infinite transformations and their inverses. https://arxiv.org/abs/1408.2445

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