Slow entropy and differentiable models for infinite-measure preserving Z^k actions
Dynamical Systems
2014-09-23 v2
Abstract
We define "slow" entropy invariants for Z^2 actions on infinite measure spaces, which measures growth of itineraries at subexponential scales. We use this to construct infinite-measure preserving Z^2 actions which cannot be realized as a group of diffeomorphisms of a compact manifold preserving a Borel measure, contrary to the situation for Z-actions, where every infinite-measure preserving action can be realized in this way.
Cite
@article{arxiv.1105.4677,
title = {Slow entropy and differentiable models for infinite-measure preserving Z^k actions},
author = {Michael Hochman},
journal= {arXiv preprint arXiv:1105.4677},
year = {2014}
}
Comments
20 pages