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Observational analysis identifies open dense subsets in quasi-periodic cocycles, highlighting the significance of Lyapunov exponents and accelerations.
We demonstrate the existence of an open dense subset within the class of real analytic one-frequency quasi-periodic (4,R)-cocycles, characterized by either the distinctness of all their Lyapunov exponents or the non-zero nature of all their accelerations, which partially answers an open problem raised by A. Avila.
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Wang et al. (2025) studied this question.
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