6533b82afe1ef96bd128b851
RESEARCH PRODUCT
Overlapping self-affine sets of Kakeya type
Pablo ShmerkinAntti Käenmäkisubject
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 mathematicsMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-06-01 | Ergodic Theory and Dynamical Systems |