6 citations · 12 across the 6 of their papers we have counts for
10 papers
On the Rajchman property for self-similar measures on
Ariel Rapaport
We establish a complete algebraic characterization of self-similar iterated function systems on , for which there exists a positive probability vector so th…
Exact dimensionality and Ledrappier-Young formula for the Furstenberg measure
Ariel Rapaport
Assuming strong irreducibility and proximality, we prove that the Furstenberg measure, corresponding to a finitely supported measure on the general linear group of a finite dimensi…
Proof of the exact overlaps conjecture for systems with algebraic contractions
Ariel Rapaport
We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.
Dimension of ergodic measures projected onto self-similar sets with overlaps
Thomas Jordan, Ariel Rapaport
For self-similar sets on satisfying the exponential separation condition we show that the natural projections of shift invariant ergodic measures is equal to $\min\{1,…
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…
On self-similar measures with absolutely continuous projections and dimension conservation in each direction
Ariel Rapaport
Relying on results due to Shmerkin and Solomyak, we show that outside a -dimensional set of parameters, for every planar homogeneous self-similar measure , with strong separa…