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Invariant measures for higher-rank hyperbolic abelian actions. (English) Zbl 0859.58021

Ergodic Theory Dyn. Syst. 16, No. 4, 751-778 (1996); correction ibid. 18, No. 2, 503-507 (1998).
The authors investigate invariant ergodic measures for certain partially hyperbolic and Anosov actions of \(\mathbb{R}^k\), \(\mathbb{Z}^k\) and \(\mathbb{Z}^k_+\). It is shown that they are either Haar measures or that every element of the action has zero metric entropy. A conjecture is established that this result may be fairly extended.
Reviewer: J.Ombach (Kraków)

MSC:

37D99 Dynamical systems with hyperbolic behavior
37A99 Ergodic theory
54C70 Entropy in general topology
54H15 Transformation groups and semigroups (topological aspects)
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