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Generalisations of the Euler adic

Published online by Cambridge University Press:  22 October 2010

GABRIEL STRASSER
GABRIEL STRASSER*
Affiliation:
Mathematics Institute, University of Vienna, Nordbergstrasse 15, A-1090 Vienna. e-mail: gabriel.strasser@univie.ac.at
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Abstract

We consider generalisations of the so-called Euler adic and investigate dynamical properties like ergodicity and total ergodicity. We prove the existence of a unique fully-supported ergodic measure for these generalisations. We also investigate the structure of non-fully-supported ergodic measures and in addition show that each of these measures (fully- and non-fully-supported) is also totally ergodic. In order to determine these dynamical properties we find closed-form expressions for the generalised Eulerian numbers. Additionally we extend a result given by Frick and Petersen to a wider class of adic transformations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 150 , Issue 2 , March 2011 , pp. 241 - 256
Copyright
Copyright © Cambridge Philosophical Society 2010

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References

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