The Lyapunov exponents of generic skew-product compact semiflows

Bessa, Mário; Carvalho, Glória Ferreira

http://hdl.handle.net/10400.2/13846

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Authors

Bessa, Mário

Carvalho, Glória Ferreira

Abstract(s)

Let F_K denote the set of infinite-dimensional cocycles over a μ-ergodic flow φ^t : M → M and with fiber dynamics given by a compact semiflow on a Hilbert space. We prove that there exists a residual subset R of F_K such that for 􏰤 φ ∈ R and for μ-almost every x ∈ M, either: (i) the limit operator lim (φ^t(x)^*φ^t(x))^(1/2t) when t→∞ is the null operator or else (ii) the Oseledets–Ruelle splitting of 􏰤 along the φ^t -orbit of x has a dominated splitting.