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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Invariant measures for general(ized) induced transformations


Author: Roland Zweimüller
Journal: Proc. Amer. Math. Soc. 133 (2005), 2283-2295
MSC (2000): Primary 28D05, 28D20, 37A05, 60G10, 60G40
Published electronically: March 14, 2005
MathSciNet review: 2138871
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Abstract: We show that the general(ized) induced transformation $T^{\tau}$ derived from an ergodic measure preserving transformation $T$ by means of an inducing time $\tau$ has an invariant measure canonically related to that of the original system iff a suitable induced version of $\tau$ is integrable. Moreover, we prove an Abramov-type entropy formula.


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Additional Information

Roland Zweimüller
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Email: r.zweimueller@imperial.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07772-5
PII: S 0002-9939(05)07772-5
Received by editor(s): July 23, 2003
Published electronically: March 14, 2005
Additional Notes: This research was partially supported by the Austrian Science Foundation FWF, project P14734-MAT, and by an APART [Austrian programme for advanced research and technology] fellowship of the Austrian Academy of Sciences.
Communicated by: Michael Handel
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.