Abstract
In [23], H.H. Rugh gave a new and simpler method to prove existence of an invariant measure with nice mixing properties for some weakly coupled analytic maps. He proved in fact a spectral gap property for a well-defined transfer operator. We modify this method to construct generalized transfer operators associated to potentials and preserve the spectral gap for small potentials. This allows us to prove new limit results for these systems: Central Limit Theorem, Moderate Deviations Principle and a partial Large Deviations result. These results are available under wide classes of observables and initial measures.
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