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Complete regularity of linear cocycles and the Baire category of the set of Lyapunov-Perron regular points
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Complete regularity of linear cocycles and the Baire category of the set of Lyapunov-Perron regular points
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Complete regularity of linear cocycles and the Baire category of the set of Lyapunov-Perron regular points
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Journal Article
Complete regularity of linear cocycles and the Baire category of the set of Lyapunov-Perron regular points
2026
Overview
Given a continuous linear cocycle$\\mathcal {A}$over a homeomorphism f of a compact metric space X , we investigate its set$\\mathcal {R}$of Lyapunov-Perron regular points, that is, the collection of trajectories of f that obey the conclusions of the Multiplicative Ergodic Theorem. We obtain results roughly saying that the set$\\mathcal {R}$is of first Baire category (i.e., meager) in X , unless some rigid structure is present. In some settings, this rigid structure forces the Lyapunov exponents to be defined everywhere and to be independent of the point; that is what we call complete regularity.
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