Search results for "local dimension"

showing 2 items of 2 documents

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

Ledrappier-Young formula and exact dimensionality of self-affine measures

2017

In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula. peerReviewed

local dimensionPlane (geometry)General MathematicsOpen problem010102 general mathematicsMathematical analysista111Dynamical Systems (math.DS)01 natural sciencesMeasure (mathematics)self-affine set010101 applied mathematicsIterated function systemself-affine measureHausdorff dimension37C45 28A80FOS: MathematicsApplied mathematicsAffine transformation0101 mathematicsMathematics - Dynamical Systemshausdorff dimensionMathematicsCurse of dimensionality
researchProduct