12 citations · 30 across the 12 of their papers we have counts for
16 papers
On self-affine measures associated to strongly irreducible and proximal systems
Ariel Rapaport
Let be a self-affine measure on associated to an affine IFS and a positive probability vector . Suppose that the maps in do not have a common fixed…
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…
Self-similar measures associated to a homogeneous system of three maps
Ariel Rapaport, Péter P. Varjú
We study the dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on and other more general IFS's. We e…
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…
Geometric Law for Multiple Returns until a Hazard
Yuri Kifer, Ariel Rapaport
For a -mixing stationary process we consider the number of multiple recurrencies to a set for u…
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…
A self-similar measure with dense rotations, singular projections and discrete slices
Ariel Rapaport
We construct a planar homogeneous self-similar measure, with strong separation, dense rotations and dimension greater than , such that there exist lines for which dimension cons…
A dimension gap for continued fractions with independent digits - the non stationary case
Ariel Rapaport
We show there exists a constant such that the dimension of every measure on , which makes the digits in the continued fraction expansion independent, is at most…
On self-affine measures with equal Hausdorff and Lyapunov dimensions
Ariel Rapaport
Let be a self-affine measure on associated to a self-affine IFS and a probability vector . Assume the strong sep…
On the Hausdorff and packing measures of slices of dynamically defined sets
Ariel Rapaport
Let be integers, and let be a self-similar set satisfying the strong separation condition, and with . We study the a.s. values of th…
Compound Poisson statistics in conventional and nonconventional setups
Ariel Rapaport
Given a periodic point in a -mixing shift with countable alphabet, the sequence of random variables counting the number of multiple returns to shrinking cylindri…
Poisson and Compound Poisson Approximations in a Nonconventional Setup
Yuri Kifer, Ariel Rapaport
We show that for all -mixing shifts distributions of the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of all points are close either to Poisson or to…