منابع مشابه
The Graduate School THERMODYNAMIC FORMALISM AND MULTIFRACTAL
We investigate to what degree results in dimension theory and multifractal formalism can be derived as a direct consequence of thermodynamic properties of a dynamical system. We show that under quite general conditions, various multifractal spectra (the entropy spectrum for Birkhoff averages and the dimension spectrum for pointwise dimensions, among others) may be obtained as Legendre transform...
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There are strong reasons to believe that the multifractal spectrum of DLA shows anomalies which have been termed left sided ME, M]. In order to show that this is compatible with strictly multiplicative structures Mandelbrot et al. M, MEH] introduced a one parameter family of multifractal measures invariant under innnitely many linear maps on the real line. Under the assumption that the usual mu...
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In this paper we prove that the conjectures of Frisch and Parisi in 9] and Arneodo et al in 1] (called the multifractal formalism for functions) may fail for some non homogenous selfsimilar functions in m dimension, m 2. In these cases, we compute the correct spectrum of singularities and we show how the multifractal formalism must be modiied.
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This article fits in many studies of multifractal analysis of measure [1, 2, 3, 4, 6, 7, 8, 9]. We took as a starting point the work of F. Ben Nasr in [2] to give a new inequality involving Dim(X α ) which would be, in certain cases, finer than the inequality Dim(X α ) ≤ inf q≥0 (αq +Bμ(q)), established by L. Olsen in [6]. Besides we elaborated an application of our result which gives a better ...
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In an earlier paper MR] the authors introduced the inverse measure y (dt) of a given measure (dt) on 0; 1] and presented thèinversion formula' f y () = f(1==) which was argued to link the respective multifractal spectra of and y. A second paper RM2] established the formula under the assumption that and y are continuous measures. Here, we investigate the general case which reveals telling detail...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2009
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089509990279