Slow entropy and differentiable models for infinite-measure preserving Z^k actions

Details Slow entropy and differentiable models for infinite-measure preserving Z^k actions Slow entropy and differentiable models for infinite-measure preserving Z^k actions

2011-05-24

arxiv.org/abs/1105.4677v2

Mathematics

Dynamical Systems

20 pages

Scientific paper

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.

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