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Mathematics > Dynamical Systems

arXiv:2202.02048 (math)
[Submitted on 4 Feb 2022 (v1), last revised 21 Sep 2022 (this version, v2)]

Title:Differentiability of the diffusion coefficient for a family of intermittent maps

Authors:Fanni M. Sélley
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Abstract:It is well known that the Liverani-Saussol-Vaienti map satisfies a central limit theorem for Hölder observables in the parameter regime where the correlations are summable. We show that when $C^2$ observables are considered, the variance of the limiting normal distribution is a $C^1$ function of the parameter. We first show this for the first return map to the base of the second branch by studying the Green-Kubo formula, then conclude the result for the original map using Kac's lemma and relying on linear response.
Comments: Version v2 is the electronic copy of the published version
Subjects: Dynamical Systems (math.DS)
Cite as: arXiv:2202.02048 [math.DS]
  (or arXiv:2202.02048v2 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.2202.02048

Submission history

From: Fanni Mincsovicsné Sélley [view email]
[v1] Fri, 4 Feb 2022 09:41:50 UTC (16 KB)
[v2] Wed, 21 Sep 2022 10:33:48 UTC (17 KB)
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