Some exceptional phenomena in multifractal formalism: Part I
Publication in refereed journal

香港中文大學研究人員

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摘要Recently it was discovered that the 3-fold convolution of the Cantor measure mu has intricate fractal structure [ HL]: the set of local dimensions mu has an isolated point and therefore the standard multifractal formalism does not hold. Our purpose here is to give a detail study of such class of examples and to understand the dilemma. This will shed some light on the multifractal structure of measures arising from iterated functions systems with overlaps, which to a large extend, is still unknown. In this Part I, we concentrate on the L(q)-spectrum tau(q); we give a formula for tau(q) and show that it is real analytic on R except for one non-differentiable point in R(-). The basic techniques are the product of matrices and the renewal theorem. In Part II, we will prove that such mu satisfies a modified multifractal formalism.
著者Lau KS, Wang XY
期刊名稱Asian Journal of Mathematics
出版年份2005
月份6
日期1
卷號9
期次2
出版社INT PRESS BOSTON, INC
頁次275 - 294
國際標準期刊號1093-6106
電子國際標準期刊號1945-0036
語言英式英語
關鍵詞Cantor measure; convolution; dimension; L(q)-spectrum; multifractal
Web of Science 學科類別Mathematics; MATHEMATICS; Mathematics, Applied; MATHEMATICS, APPLIED

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