0000000000452872

AUTHOR

Henna Koivusalo

showing 4 related works from this author

Dimensions of random affine code tree fractals

2014

We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.

Discrete mathematicsCode (set theory)v-variable fractalsApplied MathematicsGeneral MathematicsProbability (math.PR)ta111Dynamical Systems (math.DS)self-similar setsTree (descriptive set theory)Box countingFractalIterated function systemMathematics - Classical Analysis and ODEsHausdorff dimensionClassical Analysis and ODEs (math.CA)FOS: MathematicsAffine transformationMathematics - Dynamical Systems28A80 60D05 37H99RandomnessMathematics - ProbabilityMathematics
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Self-affine sets with fibered tangents

2016

We study tangent sets of strictly self-affine sets in the plane. If a set in this class satisfies the strong separation condition and projects to a line segment for sufficiently many directions, then for each generic point there exists a rotation $\mathcal O$ such that all tangent sets at that point are either of the form $\mathcal O((\mathbb R \times C) \cap B(0,1))$, where $C$ is a closed porous set, or of the form $\mathcal O((\ell \times \{ 0 \}) \cap B(0,1))$, where $\ell$ is an interval.

Pure mathematicsClass (set theory)General MathematicsDynamical Systems (math.DS)Interval (mathematics)iterated function system01 natural sciencesself-affine setGeneric pointLine segmentstrictly self-affine sets0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: MathematicsPoint (geometry)Porous set0101 mathematicsMathematics - Dynamical SystemsMathematicsApplied Mathematics010102 general mathematicsta111Tangenttangent setsTangent setMathematics - Classical Analysis and ODEs010307 mathematical physicsAffine transformation
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Dimension of self-affine sets for fixed translation vectors

2018

An affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension of the self-affine set is the affinity dimension for Lebesgue almost every translation vectors. Similar statement was proven by Jordan, Pollicott, and Simon in 2007 for the dimension of self-affine measures. In this article, we have an orthogonal approach. We introduce a class of self-affine systems in which, given translation vectors, we get the same results for Lebesgue almost all matrices. The proofs rely on Ledrappier-Young theory that was recently ver…

Pure mathematicsEuclidean spaceGeneral Mathematics010102 general mathematicsTranslation (geometry)Lebesgue integration01 natural sciencesMeasure (mathematics)010104 statistics & probabilitysymbols.namesakeIterated function systemHausdorff dimensionsymbolsAffine transformation0101 mathematicsInvariant (mathematics)MathematicsJournal of the London Mathematical Society
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Dimension of self-affine sets for fixed translation vectors

2016

An affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension of the self-affine set is the affinity dimension for Lebesgue almost every translation vectors. Similar statement was proven by Jordan, Pollicott, and Simon in 2007 for the dimension of self-affine measures. In this article, we have an orthogonal approach. We introduce a class of self-affine systems in which, given translation vectors, we get the same results for Lebesgue almost all matrices. The proofs rely on Ledrappier-Young theory that was recently ver…

Self-affine setvektoritself-affine measurevectorsmatematiikka37C45 28A80FOS: MathematicsHausdorff dimensionDynamical Systems (math.DS)Mathematics - Dynamical Systems37C45 (primary)28A80 (secondary)matemaattiset objektit
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