22 citations · 43 across the 6 of their papers we have counts for
9 papers
Dynamically defined subsets of generic self-affine sets
Balázs Bárány, Sascha Troscheit
In dynamical systems, shrinking target sets and pointwise recurrent sets are two important classes of dynamically defined subsets. In this article we introduce a mild condition on…
Hausdorff Dimension of Planar Self-Affine Sets and Measures with Overlaps
Michael Hochman, Ariel Rapaport
We prove that if is a self-affine measure in the plane whose defining IFS acts totally irreducibly on and satisfies an exponential separation condition, then it…
Hausdorff dimension of planar self-affine sets and measures
Balázs Bárány, Michael Hochman, Ariel Rapaport
Let be a strongly separated self-affine set in (or one satisfying the strong open set condition). Under mild non-compactness and irreducibility ass…
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…
On the dimension of triangular self-affine sets
Balázs Bárány, Michał Rams, Károly Simon
As a continuation of a recent work of the same authors (arXiv:1504.07138), in this note we study the dimension theory of diagonally homogeneous triangular planar self-affine IFS.
On the Ledrappier-Young formula for self-affine measures
Balázs Bárány
Ledrappier and Young introduced a relation between entropy, Lyapunov exponents and dimension for invariant measures of diffeomorphisms on compact manifolds. In this paper, we show…