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- Non-uniform hyperbolicity for infinite dimensional cocyclesPublication . Bessa, Mário; Carvalho, MariaLet H be an infinite dimensional separable Hilbert space, X a compact Hausdorff space and f : X \rightarrow X a homeomorphism which preserves a Borel ergodic measure which is positive on non-empty open sets. We prove that the non-uniformly Anosov cocycles are C0-dense in the family of partially hyperbolic f,H-skew products with non-trivial unstable bundles.
- On the Lyapunov spectrum of infinite dimensional random products of compact operatorsPublication . Bessa, Mário; Carvalho, MariaWe consider an infinite dimensional separable Hilbert space and its family of compact integrable cocycles over a dynamical system f. Assuming that f acts in a compact Hausdorff space X and preserves a Borel regular ergodic probability which is positive on non-empty open sets, we conclude that there is a C0-residual subset of cocycles within which, for almost every x, either the Oseledets–Ruelle’s decomposition along the orbit of x is dominated or all the Lyapunov exponents are equal to −∞.