Search results for " 37C45"

showing 4 items of 4 documents

Overlapping self-affine sets of Kakeya type

2009

We compute the Minkowski dimension for a family of self-affine sets on the plane. Our result holds for every (rather than generic) set in the class. Moreover, we exhibit explicit open subsets of this class where we allow overlapping, and do not impose any conditions on the norms of the linear maps. The family under consideration was inspired by the theory of Kakeya sets.

Class (set theory)Applied MathematicsGeneral Mathematics010102 general mathematicsMinkowski–Bouligand dimensionDynamical Systems (math.DS)Type (model theory)16. Peace & justice01 natural sciencesCombinatoricsSet (abstract data type)Mathematics - Classical Analysis and ODEs0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematics28A80 37C45010307 mathematical physicsAffine transformationMathematics - Dynamical Systems0101 mathematicsMathematicsErgodic Theory and Dynamical Systems
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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
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Random cutout sets with spatially inhomogeneous intensities

2015

We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures.

General MathematicsStructure (category theory)Hausdorff dimensionDynamical Systems (math.DS)01 natural sciencesMeasure (mathematics)010104 statistics & probabilityCorollaryDimension (vector space)Classical Analysis and ODEs (math.CA)FOS: MathematicsMathematics::Metric Geometry0101 mathematicsMathematics - Dynamical SystemsMathematicsmatematiikkaHausdorffin dimensioProbability (math.PR)010102 general mathematicsMathematical analysisMultifractal systemPoissonian CutoutMetric spaceMathematics - Classical Analysis and ODEsHausdorff dimensionPrimary 60D05 Secondary 28A80 37D35 37C45Intensity (heat transfer)Mathematics - Probability
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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
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