Sharp statistical properties for a family of multidimensional nonMarkovian nonconformal intermittent maps

Eslami, Peyman; Melbourne, Ian; Vaienti, Sandro

doi:10.1016/j.aim.2021.107853

Cited by 4 publications

(3 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All of the conditions of Theorem 3 are essentially verified for a first return map of f in [4]. Indeed, following [4], we can define M i = f ([0, 3 4 ]…”

Section: Example Consider the Family Of Mapsmentioning

confidence: 88%

“…Such properties include existence and properties of absolutely continuous invariant measures, decay of correlations, central limit theorem, large deviations, Berry-Esseen theorem, almost sure invariance principle, law of iterated logarithm, etc. As an example, this procedure is applied to a class of multi-dimensional intermittent maps introduced in [4], see section 4.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Inducing schemes for multi-dimensional piecewise expanding maps

Eslami¹

2022

DCDS

Self Cite

View full text Add to dashboard Cite

<p style='text-indent:20px;'>We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical properties of dynamical systems with some hyperbolicity. As an application we check the conditions for the first return map of a class of multi-dimensional non-Markov, non-conformal intermittent maps.</p>

show abstract

“…All of the conditions of Theorem 3 are essentially verified for a first return map of f in [4]. Indeed, following [4], we can define M i = f ([0, 3 4 ]…”

Section: Example Consider the Family Of Mapsmentioning

confidence: 88%

mentioning

confidence: 99%

Inducing schemes for multi-dimensional piecewise expanding maps

Eslami¹

2022

DCDS

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the second part we study the Green-Kubo formula (4) in depth, proving (5) and (6). The calculation makes use of the linear response result of [16], and takes things a few steps further to obtain continuous differentiability of σ(α).…”

Section: Proofmentioning

confidence: 99%

Differentiability of the diffusion coefficient for a family of intermittent maps

Sélley¹

2022

Preprint

View full text Add to dashboard Cite

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.

show abstract

Differentiability of the Diffusion Coefficient for a Family of Intermittent Maps

Sélley

2022

J Dyn Control Syst

View full text Add to dashboard Cite

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 C2 observables are considered, the variance of the limiting normal distribution is a C1 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.

show abstract

Sharp statistical properties for a family of multidimensional nonMarkovian nonconformal intermittent maps

Cited by 4 publications

References 62 publications

Inducing schemes for multi-dimensional piecewise expanding maps

Inducing schemes for multi-dimensional piecewise expanding maps

Differentiability of the diffusion coefficient for a family of intermittent maps

Differentiability of the Diffusion Coefficient for a Family of Intermittent Maps

Contact Info

Product

Resources

About