83 citations · 415 across the 22 of their papers we have counts for
23 papers
Projections of self-affine sets onto lines
Balázs Bárány, Antti Käenmäki, István Kolossváry
We prove an all-directions Marstrand-Mattila projection theorem for self-affine measures and sets in . Under exponential separation, together with proximality and str…
Tangents and slices of self-affine carpets
Antti Käenmäki, Alex Rutar
We study the fine scaling properties of planar self-affine carpets. For Gatzouras--Lalley carpets, we give a precise formula for maximal Hausdorff dimension of a tangent in terms o…
Regularity of non-autonomous self-similar sets
Antti Käenmäki, Alex Rutar
Non-autonomous self-similar sets are a family of compact sets which are, in some sense, highly homogeneous in space but highly inhomogeneous in scale. The main purpose of this note…
Dimension of planar non-conformal attractors with triangular derivative matrices
Balázs Bárány, Antti Käenmäki
We study the dimension of the attractor and quasi-Bernoulli measures of parametrized families of iterated function systems of non-conformal and non-affine maps. We introduce a tran…
Covering number on inhomogeneous graph-directed self-similar sets
Balázs Bárány, Antti Käenmäki, Petteri Nissinen
For a strongly connected inhomogeneous graph-directed self-similar set satisfying the strong open set condition, we characterize the asymptotic behaviour of the -covering…
Minkowski dimension for measures
Kenneth J. Falconer, Jonathan M. Fraser, Antti Käenmäki
The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literatur…
Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles
Balázs Bárány, Antti Käenmäki, Ian D. Morris
In topics such as the thermodynamic formalism of linear cocycles, the dimension theory of self-affine sets, and the theory of random matrix products, it has often been found useful…
Dimension and measures on sub-self-affine sets
Antti Käenmäki, Markku Vilppolainen
We show that in a typical sub-self-affine set, the Hausdorff and the Minkowski dimensions coincide and equal the zero of an appropriate topological pressure. This gives a partial p…
Packing dimension and Ahlfors regularity of porous sets in metric spaces
Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki +3
Let be a metric measure space with an -regular measure . We prove that if is -porous, then where $\dim_{\math…
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…
A note on correlation and local dimensions
Jiaojiao Yang, Antti Käenmäki, Min Wu
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 t…
Weak separation condition, Assouad dimension, and Furstenberg homogeneity
Antti Käenmäki, Eino Rossi
We consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets s…
Self-affine sets with fibered tangents
Antti Kaenmaki, Henna Koivusalo, Eino Rossi
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 ma…
Dynamics of the scenery flow and geometry of measures
Antti Käenmäki, Tuomas Sahlsten, Pablo Shmerkin
We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version o…
Structure of distributions generated by the scenery flow
Antti Käenmäki, Tuomas Sahlsten, Pablo Shmerkin
We expand the ergodic theory developed by Furstenberg and Hochman on dynamical systems that are obtained from magnifications of measures. We prove that any fractal distribution in…
Multifractal analysis of Birkhoff averages for typical infinitely generated self-affine sets
Antti Käenmäki, Henry WJ Reeve
We develop a thermodynamic formalism for quasi-multiplicative potentials on a countable symbolic space and apply these results to the dimension theory of infinitely generated self-…
Dimensions, Whitney covers, and tubular neighborhoods
Antti Käenmäki, Juha Lehrbäck, Matti Vuorinen
Working in doubling metric spaces, we examine the connections between different dimensions, Whitney covers, and geometrical properties of tubular neighborhoods. In the Euclidean sp…
Local structure of self-affine sets
Christoph Bandt, Antti Käenmäki
The structure of a self-similar set with open set condition does not change under magnification. For self-affine sets the situation is completely different. We consider planar self…
Equilibrium states of the pressure function for products of matrices
De-Jun Feng, Antti Kaenmaki
Let be a non-trivial family of complex matrices, in the sense that for any , there exists such that $M_{…
Overlapping self-affine sets of Kakeya type
Antti Kaenmaki, Pablo Shmerkin
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 o…