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A semi-invertible operator Oseledets theorem

Published online by Cambridge University Press:  11 March 2013

CECILIA GONZÁLEZ-TOKMAN  and
ANTHONY QUAS
CECILIA GONZÁLEZ-TOKMAN
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada, V8W 3R4 email ceciliag@uvic.caaquas@uvic.ca
ANTHONY QUAS
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada, V8W 3R4 email ceciliag@uvic.caaquas@uvic.ca
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Abstract

Semi-invertible multiplicative ergodic theorems establish the existence of an Oseledets splitting for cocycles of non-invertible linear operators (such as transfer operators) over an invertible base. Using a constructive approach, we establish a semi-invertible multiplicative ergodic theorem that for the first time can be applied to the study of transfer operators associated to the composition of piecewise expanding interval maps randomly chosen from a set of cardinality of the continuum. We also give an application of the theorem to random compositions of perturbations of an expanding map in higher dimensions.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 4 , August 2014 , pp. 1230 - 1272
Copyright
Copyright ©2013 Cambridge University Press 

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