A Nonlinear Transfer Operator Theorem

Pollicott, Mark

doi:10.1007/s10955-016-1646-1

Cited by 7 publications

(3 citation statements)

References 7 publications

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“…The dimensional theory of the multiplicative subshifts and the multifractal analysis of the multiple ergodic average attract more attention and have become popular research topics in recent years (cf. [1, 3, 6, 10, 11, 16–19]). Fan, Liao, and Ma [10] obtained the Hausdorff dimension of the level set of equation (1) with for all .…”

Section: Introductionmentioning

confidence: 99%

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Hausdorff dimension of multidimensional multiplicative subshifts

Ban

Hu²,

Lai

2023

Ergod. Th. Dynam. Sys.

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The purpose of this study is two-fold. First, the Hausdorff dimension formula of the multidimensional multiplicative subshift (MMS) in $\mathbb {N}^d$ is presented. This extends the earlier work of Kenyon et al [Hausdorff dimension for fractals invariant under multiplicative integers. Ergod. Th. & Dynam. Sys.32(5) (2012), 1567–1584] from $\mathbb {N}$ to $\mathbb {N}^d$ . In addition, the preceding work of the Minkowski dimension of the MMS in $\mathbb {N}^d$ is applied to show that their Hausdorff dimension is strictly less than the Minkowski dimension. Second, the same technique allows us to investigate the multifractal analysis of multiple ergodic average in $\mathbb {N}^d$ . Precisely, we extend the result of Fan et al, [Multifractal analysis of some multiple ergodic averages. Adv. Math.295 (2016), 271–333] of the multifractal analysis of multiple ergodic average from $\mathbb {N}$ to $\mathbb {N}^d$ .

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Section: Introductionmentioning

confidence: 99%

“…19 [11,. Theorem 7.11] If α = P ϕ (±∞), then E(α) = ∅ and dim H E(P ϕ (±∞)) = P * ϕ (P ϕ (±∞)) (p 1 • • • p d ) −1 log m .…”

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confidence: 99%

Hausdorff dimension of multidimensional multiplicative subshifts

Ban

Hu²,

Lai

2023

Ergod. Th. Dynam. Sys.

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“…Later, the multifractal analysis and the dimension theory of the multiple ergodic averages AnF(x) N in N (or Z) are also interesting research subjects and have been studied in depth recently (cf. [1,2,5,12,13,17,18,19,20]). We also refer the reader to [10] for the survey of this subject and find the complete bibliography therein.…”

Section: Introductionmentioning

confidence: 99%

Large Deviation Principle of Multidimensional Multiple Averages on $\mathbb{N}^d$

Ban,

Hu,

Lai

2021

Preprint

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This paper establishs the large deviation principle (LDP) for multiple averages on N d . We extend the previous work of [Carinci et al., Indag. Math. 2012] to multidimensional lattice N d for d ≥ 2. The same technique is also applicable to the weighted multiple average launched by Fan [Fan, Adv. Math. 2021]. Finally, the boundary conditions are imposed to the multiple sum and explicit formulae of the energy functions with respect to the boundary conditions are obtained.

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On the Entropy of Multidimensional Multiplicative Integer Subshifts

Ban

Lai

2021

J Stat Phys

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A Nonlinear Transfer Operator Theorem

Cited by 7 publications

References 7 publications

Hausdorff dimension of multidimensional multiplicative subshifts

Hausdorff dimension of multidimensional multiplicative subshifts

Large Deviation Principle of Multidimensional Multiple Averages on $\mathbb{N}^d$

On the Entropy of Multidimensional Multiplicative Integer Subshifts

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