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首页> 外文期刊>Discrete and continuous dynamical systems >LOCALIZED ASYMPTOTIC BEHAVIOR FOR ALMOST ADDITIVE POTENTIALS
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LOCALIZED ASYMPTOTIC BEHAVIOR FOR ALMOST ADDITIVE POTENTIALS

机译：几乎所有加性势的局部渐近行为

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摘要

We conduct the multifractal analysis of the level sets of the asymptotic behavior of almost additive continuous potentials (φ_n)_(n=1)~∞ on a topolog-ically mixing subshift of finite type X endowed itself with a metric associated with such a potential. We work without additional regularity assumption other than continuity. Our approach differs from those used previously to deal with this question under stronger assumptions on the potentials. As a consequence, it provides a new description of the structure of the spectrum in terms of weak concavity. Also, the lower bound for the spectrum is obtained as a consequence of the study sets of points at which the asymptotic behavior of φ_n (x) is localized, i.e. depends on the point x rather than being equal to a constant. Specifically, we compute the Hausdorff dimension of sets of the form {x ∈ X : lim_(n→∞ φ_n)(x) = ξ(x)}, where ξ is a given continuous function. This has interesting geometric applications to fixed points in the asymptotic average for dynamical systems in R~d, as well as the fine local behavior of the harmonic measure on conformal planar Cantor sets.
机译：我们对赋给自身的有限类型X的拓扑混合子移位进行近似加性连续势（φ_n）_（n = 1）〜∞的渐近行为的水平集的多重分形分析。 。除了连续性之外，我们无需其他常规性假设即可工作。我们的方法不同于以前在潜力更大的假设下用于处理此问题的方法。结果，它以弱凹度提供了对光谱结构的新描述。而且，由于研究点的集合而获得了频谱的下界，在这些研究点处，φ_n（x）的渐近行为位于局部，即，取决于点x而不是等于常数。具体来说，我们计算{x∈X：lim_（n→∞φ_n）（x）/ n =ξ（x）}形式的集合的Hausdorff维数，其中ξ是给定的连续函数。这对于R〜d中动力系统的渐近平均中的不动点具有有趣的几何应用，以及在保形平面Cantor集上谐波测度的精细局部行为。

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