Key points are not available for this paper at this time.
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^-stably exhibits bounded orbits (>0). The proof is based on a new mechanism which yields stable elliptic-type behavior in arbitrary dimensions.
Nassiri et al. (Sun,) studied this question.