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Invariant densities for generalized β-maps

Published online by Cambridge University Press:  01 October 2007

PAWEŁ GÓRA
PAWEŁ GÓRA*
Affiliation:
Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec H3G 1M8, Canada (email: pgora@mathstat.concordia.ca)
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Abstract

We find an explicit formula for the invariant density of a generalized β-map. This allows us to also find an explicit formula for the invariant density of Chebyshev map and discuss the monotonicity of the asymptotic average for such maps. Our results are based on a generalization of works of Parry (Acta Math. Acad. Sci. Hungar. 11 (1960), 401–416; 15 (1964), 95–105).

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 5 , October 2007 , pp. 1583 - 1598
Copyright
Copyright © Cambridge University Press 2007

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