Self-similar vector-valued measures☆

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Abstract

The self-similar vector-valued measure is a vector analogue of the self-similar measure. In this paper we consider its multifractal structure. We show that the multifractal formalism holds if the iterated function system (IFS) involved satisfies the open set condition. This result can be applied to the study of the multifractal formalism of certain self-similar IFS with overlaps.

MSC

28A78
28A80

Keywords

Self-similar vector-valued measure
Multifractal structure
The open set condition
Pressure function
Young measure

Cited by (0)

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The research was partially supported by the NSF of China (10471049), the Project-sponsored by SRF for ROCS, SEM.

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