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- W1635336334 abstract "The multifractal spectrum of a Borel measure $mu$ in $mathbb{R}^n$ is defined as [ f_mu(alpha) = dim_H {x:lim_{rto 0} frac{log mu(B(x,r))}{log r}=alpha}. ] For self-similar measures under the open set condition the behavior of this and related functions is well-understood; the situation turns out to be very regular and is governed by the so-called ''multifractal formalism''. Recently there has been a lot of interest in understanding how much of the theory carries over to the overlapping case; however, much less is known in this case and what is known makes it clear that more complicated phenomena are possible. Here we carry out a complete study of the multifractal structure for a class of self-similar measures with overlap which includes the 3-fold convolution of the Cantor measure. Among other things, we prove that the multifractal formalism fails for many of these measures, but it holds when taking a suitable restriction." @default.
- W1635336334 created "2016-06-24" @default.
- W1635336334 creator A5078951763 @default.
- W1635336334 date "2004-08-03" @default.
- W1635336334 modified "2023-09-27" @default.
- W1635336334 title "A Modified Multifractal Formalism for a Class of Self-Similar Measures" @default.
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