## Abstract

We define slow entropy invariants for Z ^{d} actions on infinite measure spaces, which measure growth of itineraries at subexponential scales. We use this notion 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, in contrast to the situation for Z actions, where every infinite-measure preserving action can be realized in this way.

Original language | American English |
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Pages (from-to) | 653-674 |

Number of pages | 22 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 32 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2012 |

Externally published | Yes |

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