Holder continuity of Oseledets splittings for semi-invertible operator cocycles

摘要

For Holder continuous cocycles over an invertible, Lipschitz base, we establish the Holder continuity of Oseledets subspaces on compact sets of arbitrarily large measure. This extends a result of Araujo et al [On Holder-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.