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We establish conditions for aperiodicity of cocycles (in the sense of 12), obtaining, via a study of perturbations of transfer operators, conditional local limit theorems and exactness of skew-products. Our results apply to a large class of Markov and non-Markov interval maps, including beta transformations. This allows us to establish various stochastic properties of beta expansions.
Aaronson et al. (Mon,) studied this question.
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