Doubling properties of self-similar measures
Webtask dataset model metric name metric value global rank remove Webterize, in these examples, the weights for which the self-similar measure is doubling on the attractor. To name a few, the first example represents a case where there is a …
Doubling properties of self-similar measures
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WebFeb 1, 2024 · Actually, in terms of all known self-similar spectral measures, after some rearrangement, the condition (⁎) is true. Theorem 1.5. Let 0 < ρ < 1 and let D ⊂ Z be a … WebJan 1, 2007 · These measures form a subclass of absolutely continuous doubling measures on R n . Examples of singular doubling measures can be obtained from self …
Webthan having a limsup of full µ-measure when µ is not doubling, as suggested by the following lemma proved in [13], and whose second item will be used to apply our main … WebJul 24, 2024 · quasi-doubling of self-similar measures 7 In this article we will focus o n the quasi-Assouad dimension and will show that various desirable properties ho ld under …
Websystem, or WIFS, and µ the corresponding invariant self-similarmeasure. Studying the properties of self-similar measures, and in particular quantifying their smoothness, is a … WebAs is well known, when a self-similar set satisfies the strong separation condition, all self-similar measures are doubling. In this paper, we further prove that all Markov measures are doubling on a self-similar set with the strong separation condition. Subsequently, we focus on self-similar measures and Markov measures on Sierpinski carpets.
WebAs is well known, when a self-similar set satisfies the strong separation condition, all self-similar measures are doubling. In this paper, we further prove that all Markov …
WebTitle: Doubling properties of self-similar measures. Authors: Po-Lam Yung. Issue: Volume 56 (2007), Issue 2, 965-990. Abstract: Let $\{F_i\}_{i=1}^N$ be a system of similitudes in $\mathbb{R}^n$. We study necessary and sufficient conditions for their associated self-similar measures to be doubling on its support. rightful godWebJul 24, 2024 · Our main focus is on self-similar measures in whose support is an interval and which may have `overlaps'. For measures that satisfy a weaker condition than the … rightful kingWebDec 21, 2024 · The doubling properties of self-similar measures are quite well studied. The fact that self-similar measures satisfying the SSC are doubling follows, for example, from proposition 4.8 , and as mentioned in remark 5.5 , their Assouad dimension was explicitly computed by Fraser and Howroyd [ Reference Fraser and Howroyd 10 ], and it … rightful duke of milan crosswordWebDoubling properties of self-similar measures. - CORE Reader rightful german territoryWebJan 23, 2024 · In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation. This result shows that for a family of limsup sets, their Lebesgue measure is determined by the convergence or divergence of naturally occurring volume … rightful heir definedWebto us by simply studying properties of self-similar measures. Last of all, we introduce a property of an iterated function system that we call being ... dimension and absolute continuity of self-similar measures. In this paper we make progress with each of these goals. Theorems 2.2, 2.6 and 2.9 address the ... rightful heir tngWebas the usual Cantor measure, showing in some cases that averages such as (1.1) HiR) = -^[ \pix)\2dx R P J\x\ oo, where n is the dimension of the Euclidean space R" on which p is defined and ß is a kind of dimension determined by the self-similarity properties of p. rightful home