k-RATIONAL APPROXIMATIONS IN k-LüROTH EXPANSIONS

Erik Contreras

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k-RATIONAL APPROXIMATIONS IN k-LüROTH EXPANSIONS

机译：k-lüroth扩展中的K理性近似值

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In this article, we study a one parameter family of numerical systems called k-Lüroth expansions. Every irrational number has an infinite expansion and associated to it, there is a sequence of k-rational approximations. We are interested in the size of sets of points having the same exponential speed of approximations by k-rationals for different values of k. We prove that the Hausdorff dimension of these sets varies analytically with respect to the parameter k. Our techniques come from ergodic theory, in particular thermodynamic formalism for countable Markov shifts. The obtained results are contributions to multifractal analysis theory.

机译：在本文中，我们研究了一个名为k-lüroth扩展的数值系统的参数家族。每个非理性数量都有无限的扩展，并且与之相关，有一系列K理性近似值。我们对具有k理性的近似值的指数速度相同的指数速度的尺寸感兴趣。我们证明，这些集合的Hausdorff维度在参数k方面分析上有所不同。我们的技术来自厄贡理论，尤其是可计数马尔可夫转移的热力学形式主义。获得的结果是对多重分析理论的贡献。

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《Far east journal of mathematical sciences》 |2021年第1期|67-87|共21页
作者
Erik Contreras;
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作者单位

Pontificia Universidad Católica de Chile Vicu?a Mackenna 4860, Macul Región Metropolitana, Chile;

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原文格式 PDF
正文语种英语
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关键词
Irrational number; Hausdorff dimension; SETTINGone-parameterapproximation;

机译：非理性数字;豪斯多夫尺寸;sethone-parameterApproximation;

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k-RATIONAL APPROXIMATIONS IN k-LüROTH EXPANSIONS

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