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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 [email protected]@uvic.ca
ANTHONY QUAS
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada, V8W 3R4 email [email protected]@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.

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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