On the Lyapunov spectrum of infinite dimensional random products of compact operators

Bessa, Mário; Carvalho, Maria

http://hdl.handle.net/10400.2/13902

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Authors

Bessa, Mário

Carvalho, Maria

Abstract(s)

We 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 −∞.

Keywords

Random operators Dominated splitting Multiplicative ergodic theorem Lyapunov exponents

URI

http://hdl.handle.net/10400.2/13902

Citation

M. Bessa, M. Carvalho, On the Lyapunov spectrum of infinite dimensional random products of compact operators, Stochastics and Dynamics, 8, 4, 593-611, 2011