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Mosc. Math. J., 2014, Volume 14, Number 2, Pages 385–423 (Mi mmj527)  

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

Abstract: 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.

DOI: https://doi.org/10.17323/1609-4514-2014-14-2-385-423

Full text: http://www.mathjournals.org/.../2014-014-002-010.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 37F35, 37A99, 22F10
Received: March 7, 2013; in revised form September 27, 2013
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Citation: 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
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\by Julio~C.~Rebelo
\paper On the higher ergodic theory of certain non-discrete actions
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 2
\pages 385--423
\mathnet{http://mi.mathnet.ru/mmj527}
\crossref{https://doi.org/10.17323/1609-4514-2014-14-2-385-423}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3236499}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000342789300010}


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