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Moscow Mathematical Journal

Volume 14, Issue 2, April–June 2014  pp. 385–423.

On the Higher Ergodic Theory of Certain Non-Discrete Actions

Authors:  Julio C. Rebelo
Author institution:Institut de Mathématiques de Toulouse, Université de Toulouse, 118 Route de Narbonne F-31062, Toulouse, FRANCE


Quasi-invariant measures for non-discrete groups of diffeomorphisms containing a Morse–Smale dynamics are studied. The assumption concerning the presence of a Morse–Smale dynamics allows us to extend to higher dimensions a number of recently established results for non-discrete groups acting on the circle. The last section of this paper discusses the connection between these results and a few interesting questions about rigidity of continuous and non-continuous orbit equivalences for many groups as above.

2010 Mathematics Subject Classification. 37F35, 37A99, 22F10.

Keywords: Non-discrete groups, topological rigidity, quasi-invariant measures.

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