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arXiv · 1603.01421

H\"older continuity of Oseledets splittings for semi-invertible operator cocycles

Davor Dragičević·Gary Froyland
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Abstract

For H\"older continuous cocycles over an invertible, Lipschitz base, we establish the H\"older continuity of Oseledets subspaces on compact sets of arbitrarily large measure. This extends a result of Ara\'{u}jo, Bufetov, and Filip by considering possibly noninvertible 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 noninvertible cocycle with nonvanishing Lyapunov exponents exhibits nonuniformly hyperbolic behaviour (in the sense of Pesin) on a set of full measure.

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Davor Dragičević, Gary Froyland. 2016-03-04. H\"older continuity of Oseledets splittings for semi-invertible operator cocycles. https://doi.org/10.1017/etds.2016.55

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