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Slow entropy and differentiable models for infinite-measure preserving ℤk actions
Published online by Cambridge University Press: 17 January 2012
Abstract
We define ‘slow’ entropy invariants for ℤd actions on infinite measure spaces, which measure growth of itineraries at subexponential scales. We use this notion to construct infinite-measure preserving ℤ2 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.
- Type
- Research Article
- Information
- Ergodic Theory and Dynamical Systems , Volume 32 , Issue 2: Daniel J. Rudolph – in Memoriam , April 2012 , pp. 653 - 674
- Copyright
- Copyright © Cambridge University Press 2012
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