Search results for "Moran construction"

showing 3 items of 3 documents

Weakly controlled Moran constructions and iterated functions systems in metric spaces

2011

We study the Hausdorff measures of limit sets of weakly controlled Moran constructions in metric spaces. The separation of the construction pieces is closely related to the Hausdorff measure of the corresponding limit set. In particular, we investigate different separation conditions for semiconformal iterated function systems. Our work generalizes well known results on self-similar sets in metric spaces as well as results on controlled Moran constructions in Euclidean spaces.

Pure mathematicsClosed set28A8028A80 28A78 (Primary); 37C45 (Secondary)General MathematicsHausdorff dimensionDynamical Systems (math.DS)Hausdorff measureCombinatoricsopen set conditionsemikonforminen iteroitu funktiojärjestelmäsemiconformal iterated function systemFOS: Mathematics37C45 (Secondary)Hausdorff measureHausdorff-ulottuvuusMathematics - Dynamical SystemsHausdorffin mittaMathematicsball condition37C45avoimen joukon ehtoMoran-konstruktiofinite clustering propertyInjective metric spaceHausdorff spaceMoran constructionäärellinen pakkautuminenConvex metric space28A80 28A78 (Primary)Metric spaceHausdorff distance28A78palloehtoNormal space
researchProduct

A note on correlation and local dimensions

2015

Abstract Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.

Correlation dimensionPure mathematicslocal dimensionfinite clustering propertyGeneral MathematicsApplied Mathematics010102 general mathematicsta111General Physics and AstronomyStatistical and Nonlinear Physics01 natural sciencescorrelation dimension010305 fluids & plasmasSet (abstract data type)CombinatoricsCorrelationmoran constructionMathematics - Classical Analysis and ODEs0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsLimit setConstruct (philosophy)Mathematics
researchProduct

Weak separation condition, Assouad dimension, and Furstenberg homogeneity

2015

We consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets satisfying the weak separation condition and certain sub-self-affine sets. In addition to dimension results for the limit set, we manage to express the Assouad dimension of any closed subset of a self-conformal set by means of the Hausdorff dimension. As an interesting consequence of this, we show that a Furstenberg homogeneous self-similar set in the real line satisfies the weak separation condition. We also exhibit a self-similar set which satisfies the open set condition but fails to be Furstenberg homogeneous.

General MathematicsHomogeneity (statistics)ta111Open setPrimary 28A80 Secondary 37C45 28D05 28A50Moran constructioniterated function systemSet (abstract data type)CombinatoricsDimension (vector space)dimensionMathematics - Classical Analysis and ODEsweak separation conditionClassical Analysis and ODEs (math.CA)FOS: MathematicsLimit (mathematics)Limit setCluster analysisReal lineMathematics
researchProduct