Hölder continuity of Oseledets splittings for semi-invertible operator cocycles

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 cons...

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Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 38; no. 3; pp. 961 - 981
Main Authors DRAGIČEVIĆ, DAVOR, FROYLAND, GARY
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.05.2018
Subjects
Continuity (mathematics)
Hilbert space
Liapunov exponents
Operators (mathematics)
Original Article
Subspaces
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Summary: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2016.55