0000000000191473

AUTHOR

Markku Vilppolainen

showing 2 related works from this author

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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Separation conditions on controlled Moran constructions

2017

It is well known that the open set condition and the positivity of the $t$-dimensional Hausdorff measure are equivalent on self-similar sets, where $t$ is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions with this respect.

Class (set theory)Pure mathematicsAlgebra and Number Theory010102 general mathematicsSeparation (statistics)Zero (complex analysis)Open setDynamical Systems (math.DS)01 natural sciencesTopological pressure0103 physical sciencesFOS: MathematicsQuantitative Biology::Populations and EvolutionHausdorff measure010307 mathematical physicsMathematics - Dynamical Systems0101 mathematicsMathematicsFundamenta Mathematicae
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