This is the first part of a series of papers devoted to the study of linear cocycles over chaotic systems. In the present paper, we show that every SL(d,R) cocycle over a shift of finite type either admits a dominated splitting or is C⁰-approximated by a cocycle that C^α-stably exhibits bounded orbits (α>0). The proof is based on a new mechanism which yields stable elliptic-type behavior in arbitrary dimensions.
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Nassiri et al. (2024) studied this question.
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