Search results for "Iterated function system"

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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
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