Singularity of Fractal Measure Associated with The $(0, 1, 7)$ - Problem

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Singularity of Fractal Measure Associated with The $(0, 1, 7)$ - Problem

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dc.contributor.author Truong, Thi Thuy Duong
dc.contributor.author Vu, Hong Thanh
dc.date.accessioned 2011-04-18T09:10:48Z
dc.date.available 2011-04-18T09:10:48Z
dc.date.issued 2005
dc.identifier.citation VNU. JOURNAL OF SCIENCE, Mathematics - Physics. T.XXI, N02 - 2005 vi
dc.identifier.issn 0866-8612
dc.identifier.uri http://hdl.handle.net/123456789/474
dc.description VNU. JOURNAL OF SCIENCE, Mathematics - Physics. Vol. 21,No. 2 - 2005 vi
dc.description.abstract Let μ be the probability measure induced by S = 􀀟 ∞n =1 3−nXn, where X1,X2, ... is a sequence of independent, identically distributed (i.i.d) random variables each taking values 0, 1, a with equal probability 1/3. Let α(s) (resp.α(s), α(s)) denote the local dimension (resp. lower, upper local dimension) of s ∈ supp μ, and let α = sup{α(s) : s ∈ supp μ}; α = inf{α(s) : s ∈ supp μ}; E = {α : α(s) = α for some s ∈ supp μ} . In the case a = 3k +1 for k = 1, E = [1 − log(1+√5)−log 2 log 3 , 1], see [10]. It is conjectured that in the general case, for a = 3k + 1 ( k ∈ N), the local dimension is of the form as the case k = 1, i.e., E = [1 − log a b log 3 , 1] for a, b depends on k. In fact, our result shows that for k = 2 (a = 7), we have α = 1, α = 1− log(1+√3) 3 log 3 and E = [1 − log(1+√3) 3 log 3 , 1]. vi
dc.language.iso en vi
dc.publisher ĐHQGHN vi
dc.subject Fractal Measure vi
dc.title Singularity of Fractal Measure Associated with The $(0, 1, 7)$ - Problem vi
dc.type Article vi

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