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Functional norms for Young towers

Published online by Cambridge University Press:  24 August 2009

MARK F. DEMERS
MARK F. DEMERS*
Affiliation:
Department of Mathematics, Fairfield University, Fairfield CT 06824, USA (email: mdemers@fairfield.edu)
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Abstract

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We introduce functional norms for hyperbolic Young towers which allow us to directly study the transfer operator on the full tower. By eliminating the need for secondary expanding towers commonly employed in this context, this approach simplifies and expands the analysis of this class of Markov extensions and the underlying systems for which they are constructed. As an example, we prove large-deviation estimates with a uniform rate function for a large class of non-invariant measures and show how to translate these to the underlying system.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 5 , October 2010 , pp. 1371 - 1398
Copyright
Copyright © Cambridge University Press 2009

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