Geometric and combinatorial properties of self-similar multifractal measures

Multifractal formalism for self-similar measures with weak separation condition

For any self-similar measure μ on R satisfying the weak separation condition, we show that there exists an open ball U0 with μ(U0) > 0 such that the distribution of μ, restricted on U0, is controlled by the products of a family of non-negative matrices, and hence μ|U0 satisfies a kind of quasi-product property. Furthermore, the multifractal formalism for μ|U0 is valid on the whole range of dime...

Multifractal spectra for random self-similar measures via branching processes

Abstract Start with a compact set K ⊂ Rd. This has a random number of daughter sets each of which is a (rotated and scaled) copy of K and all of which are inside K. The random mechanism for producing daughter sets is used independently on each of the daughter sets to produce the second generation of sets, and so on, repeatedly. The random fractal set F is the limit, as n goes to infinity, of th...

Is Network Traac Self-similar or Multifractal?

This note addresses the question of whether self-similar processes are suucient to model packet network traac, or whether a broader class of multifractal processes is needed. By using the absolute moments of aggregate traac measurements , we conclude that measured local-area network (LAN) and wide-area network (WAN) traac traces, with the sample means subtracted, are well modelled by random pro...

A modified multifractal formalism for a class of self-similar measures with overlap

The multifractal spectrum of a Borel measure μ in R is defined as fμ(α) = dimH { x : lim r→0 logμ(B(x, r)) log r = α }

Self-Similar Measures