Hausdorff measures for a class of homogeneous Moran sets

Qu, Cheng-qin; Zhou, Zheng‐Jun

doi:10.1016/j.na.2005.09.002

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2010

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“…Recently, the exact value of the Hausdorff measure for a class of regular homogeneous Moran sets with Hausdorff dimension greater than one was calculated (cf. [19]). Moreover, an effective method for computing the exact value of the Hausdorff measure of a class of self-similar fractal sets has been provided (cf.…”

Section: Introductionmentioning

confidence: 99%

Hausdorff measure of uniform self-similar fractals

Kreitmeier

2010

Anal. Theory Appl.

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Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on R d . Denote by D the Hausdorff dimension, by H D (E) the Hausdorff measure and by diam(E) the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and H D (E) = diam(E) D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover we present a parametrised UIFS where ω depends on c and H D (E) < diam(E) D , if c is small enough. MSC(2010): 28A80, 28A78

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Section: Introductionmentioning

confidence: 99%

Hausdorff measure of uniform self-similar fractals

Kreitmeier

2010

Anal. Theory Appl.

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Hausdorff measures for a class of homogeneous Moran sets

Cited by 1 publication

References 10 publications

Hausdorff measure of uniform self-similar fractals

Hausdorff measure of uniform self-similar fractals

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