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Multifractal of self-conformal measures

Yuan-Ling Ye

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Recommended by J A Glazier

The vector-valued measure generated by the self-conformal iterated function system (IFS) was introduced by the author (2004 J. Math. Anal. Appl. 299 341–56). Its variation is scalar measure. This paper proves that the Lq-spectrum of the variation measure is differentiable and the corresponding multifractal formalism holds, if the relevant IFS satisfies the open set condition. This result can be applied to the study of self-conformal (scalar) measures generated by certain IFS with overlaps.


PACS

05.45.Df Fractals

MSC

28A78 Hausdorff and packing measures

28A80 Fractals (See also 37Fxx)

Subjects

Statistical physics and nonlinear systems

Dates

Issue 5 (September 2005)

Received 16 July 2004, in final form 17 May 2005

Published 1 July 2005



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