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Article Dans Une Revue Journal of the London Mathematical Society Année : 2021

Random-like properties of chaotic forcing

Résumé

We prove that skew systems with a sufficiently expanding base have approximate exponential decay of correlations, meaning that the exponential rate is observed modulo an error. The fiber maps are only assumed to be Lipschitz regular and to depend on the base in a way that guarantees diffusive behaviour on the vertical component. The assumptions do not imply an hyperbolic picture and one cannot rely on the spectral properties of the transfer operators involved. The approximate nature of the result is the inevitable price one pays for having so mild assumptions on the dynamics on the vertical component. However, the error in the approximation goes to zero when the expansion of the base tends to infinity. The result can be applied beyond the original setup when combined with acceleration or conjugation arguments, as our examples show.
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hal-03953344 , version 1 (29-05-2024)

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Paolo Giulietti, Stefano Marmi, Matteo Tanzi. Random-like properties of chaotic forcing. Journal of the London Mathematical Society, 2021, 106 (3), pp.2804-2845. ⟨10.1112/jlms.12649⟩. ⟨hal-03953344⟩
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