Multifractal analysis of ergodic averages in some non-uniformly hyperbolic systems

Yin, Zheng; Chen, Ercai; Zhou, Xiaoyao

doi:10.1017/etds.2015.14

Cited by 5 publications

(4 citation statements)

References 45 publications

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“…Barreira-Schmeling [11]. Recently Zhou and Chen [65] have show that the set of historic points carries full topological pressure for systems with non-uniform specification under certain conditions; this has been generalized by Tian-Varandas [63]. Here we have shown that wild historic points are generic in a broad class of examples.…”

Section: Conjecturessupporting

confidence: 51%

Abundance of Wild Historic Behavior

Araújo

Pinheiro

2019

Bull Braz Math Soc, New Series

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Using Caratheodory measures, we associate to each positive orbit O + f (x) of a measurable map f , a Borel measure η x . We show that η x is f -invariant whenever f is continuous or η x is a probability. These measures are used to study the historic points of the system, that is, points with no Birkhoff averages, and we construct topologically generic subset of wild historic points for wide classes of dynamical models. We use properties of the measure η x to deduce some features of the dynamical system involved, like the existence of heteroclinic connections from the existence of open sets of historic points.

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Section: Conjecturessupporting

confidence: 51%

Abundance of Wild Historic Behavior

Araújo

Pinheiro

2019

Bull Braz Math Soc, New Series

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“…We must mention that the case r = 1 was proved in [15]. However, unlike we do here, in that article the proof is not based on the saturadness.…”

Section: Introductionmentioning

confidence: 77%

On the Irregular Part ofV-Statistics Multifractal Spectra for Systems with Non-Uniform Specification

Mesón¹,

Vericat²

2015

Journal of Dynamical Systems and Geometric Theories

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Let (X, f ) be a dynamical system with X a compact metric space.Let X r be the product of r−copies of X, r ≥ 1, and Φ : X r → R. The multifractal decomposition for V −statistics for Φ, f is defined asThe set of points x ∈ X, for which the limit does not exist is called the irregular part, or historic set, of the spectrum. In this article we analyze the irregular part of the V −statistics for systems satisfying a weak form of the known Bowen specification property, called the non-uniform specification property. This concept was introduced by P. Varandas and allows to work in a nonuniformly hyperbolic context.

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“…For Banach valued continuous observable, similar variational principle was also established for system with specification property [11]. As a generalisation of above variational principle, the variational principle regarding topological pressure of M ϕ,α was also established for systems we mentioned above [26,34,40]. Meanwhile, for the above systems, the measure negligible set I ϕ carries full topological pressure [35][36][37].…”

Section: Introductionmentioning

confidence: 90%

Mechanical Property of Sn-58Bi Solder Paste Strengthened by Resin

2018

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Sn-58Bi solder has been widely used for microelectronics packaging due to its low melting point temperature, good wetting performance, good mechanical properties, and low cost. Compared with Sn-Bi solder alloy and Sn-Pb solder alloy, the strength and plasticity of Sn-Bi solder are not enough, due to the higher brittleness of bismuth, which thus limits the application of Sn-Bi solder. In order to improve the properties of Sn-Bi solder, a novel solder paste strengthened with resin was developed by mixing epoxy resin (ER) with Sn-58Bi solder, which enhanced the joint strength at a low cost. Aimed at the electronic industry, in this study, the spreadability of the novel solder paste was investigated, and the mechanical properties and microstructure of solder joints after reflow soldering were tested and analyzed. The results showed that when the content of epoxy resin was in the optimum range, the shear strength was significantly higher, reaching nearly twice that of Sn-58Bi solder alone.

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Multifractal analysis of ergodic averages in some non-uniformly hyperbolic systems

Abstract: Abstract. This article is devoted to the study of the multifractal analysis of ergodic averages in some nonuniformly hyperbolic systems. In particular, our results hold for the robust classes of multidimensional nonuniformly expanding local diffeomorphisms and Viana maps.

Cited by 5 publications

References 45 publications

Abundance of Wild Historic Behavior

Abundance of Wild Historic Behavior

On the Irregular Part ofV-Statistics Multifractal Spectra for Systems with Non-Uniform Specification

Mechanical Property of Sn-58Bi Solder Paste Strengthened by Resin

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