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Slow entropy and differentiable models for infinite-measure preserving ℤk actions

Published online by Cambridge University Press:  17 January 2012

MICHAEL HOCHMAN
MICHAEL HOCHMAN*
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Rd, Princeton, NJ 08544, USA (email: hochman@math.princeton.edu)
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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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