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Hölder continuity of Oseledets splittings for semi-invertible operator cocycles

Published online by Cambridge University Press:  09 September 2016

DAVOR DRAGIČEVIĆ  and
GARY FROYLAND
DAVOR DRAGIČEVIĆ
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia email [email protected], [email protected]
GARY FROYLAND
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia email [email protected], [email protected]
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Abstract

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For Hölder continuous cocycles over an invertible, Lipschitz base, we establish the Hölder continuity of Oseledets subspaces on compact sets of arbitrarily large measure. This extends a result of Araújo et al [On Hölder-continuity of Oseledets subspaces J. Lond. Math. Soc.93 (2016) 194–218] by considering possibly non-invertible cocycles, which, in addition, may take values in the space of compact operators on a Hilbert space. As a by-product of our work, we also show that a non-invertible cocycle with non-vanishing Lyapunov exponents exhibits non-uniformly hyperbolic behaviour (in the sense of Pesin) on a set of full measure.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 3 , May 2018 , pp. 961 - 981
Copyright
© Cambridge University Press, 2016 

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