Random-like properties of chaotic forcing

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 behavi...

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Bibliographic Details
Published inarXiv.org
Main Authors Giulietti, Paolo, Marmi, Stefano, Tanzi, Matteo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.04.2021
Subjects
Conjugation
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Summary: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.
ISSN:2331-8422