English

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.

Keywords

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}
}

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20 pages