83 citations · 415 across the 22 of their papers we have counts for
4 papers · 1 filter
Self-affine sets in analytic curves and algebraic surfaces
De-Jun Feng, Antti Käenmäki
We characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces cannot contain non-trivial self-affine sets.
Dimension of self-affine sets for fixed translation vectors
Balazs Barany, Antti Kaenmaki, Henna Koivusalo
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, Falcone…
Genericity of dimension drop on self-affine sets
Antti Käenmäki, Bing Li
We prove that generically, for a self-affine set in , removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension.…
Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
Antti Käenmäki, Ian D. Morris
A fundamental problem in the dimension theory of self-affine sets is the construction of high-dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the…