On the higher ergodic theory of certain non-discrete actions
Julio C. Rebelo
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.
Key words and phrases:
non-discrete groups, topological rigidity, quasi-invariant measures.
MSC: 37F35, 37A99, 22F10
Received: March 7, 2013; in revised form September 27, 2013
Julio C. Rebelo, “On the higher ergodic theory of certain non-discrete actions”, Mosc. Math. J., 14:2 (2014), 385–423
Citation in format AMSBIB
\paper On the higher ergodic theory of certain non-discrete actions
\jour Mosc. Math.~J.
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