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

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.

20 pages

References in corpus (3)

• A ratio ergodic theorem for multiparameter non-singular actions
• The recurrence time for ergodic systems of infinite measures
• Zero Krengel Entropy does not kill Poisson Entropy

Cited by in corpus (4)

• Metric vs topological receptive entropy of semigroup actions
• Slow Entropy of Some Parabolic Flows
• Entropy dimension of measure preserving systems
• Entropy dimension for Deterministic Walks in Random Sceneries