Oseledets splitting and invariant manifolds on fields of Banach spaces. (English) Zbl 1527.37053
J. Dyn. Differ. Equations 35, No. 1, 103-133 (2023); correction ibid. 35, No. 1, 983 (2023).
Summary: We prove a semi-invertible Oseledets theorem for cocycles acting on measurable fields of Banach spaces, i.e. we only assume invertibility of the base, not of the operator. As an application, we prove an invariant manifold theorem for nonlinear cocycles acting on measurable fields of Banach spaces.
MSC:
| 37H15 | Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents |
| 37D10 | Invariant manifold theory for dynamical systems |
Keywords:
semi-invertible multiplicative ergodic theorem; Oseledets splitting; fields of Banach spaces; invariant manifoldsReferences:
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