B. Solomyak

activity

20022026

most citedPure Point Dynamical and Diffraction Spectra

147 citations · 468 across the 45 of their papers we have counts for

collaborators

54 papers

math.DS2026

Quantitative weak mixing for typical Salem substitution suspension flows

Juan Marshall-Maldonado, Boris Solomyak

The paper investigates quantitative weak mixing of Salem substitutions flows. We prove that for a substitution whose substitution matrix is irreducible over the rationals and the d…

math.DS2025

Fourier decay and absolute continuity for typical homogeneous self-similar measures in $R^{d}$ for $d \geq 3$

Boris Solomyak

We consider iterated function systems (IFS) in $R^{d}$ for $d \geq 3$ of the form ${f_{j} (x) = λ O x + a_{j}}_{j = 0}^{m}$ , with $a_{0} = 0$ and $m \geq 1$ . Here $λ \in (0, 1)$ i…

math.DS2024

Local spectral estimates and quantitative weak mixing for substitution $Z$ -actions

Alexander I. Bufetov, Juan Marshall-Maldonado, Boris Solomyak

The paper investigates Hölder and log-Hölder regularity of spectral measures for weakly mixing substitutions and the related question of quantitative weak mixing. It is assumed tha…

math.DS2023

Absolute continuity of self-similar measures on the plane

Boris Solomyak, Adam Śpiewak

Consider an iterated function system consisting of similarities on the complex plane of the form $g_{i} (z) = λ_{i} z + t_{i}, λ_{i}, t_{i} \in C, ∣ λ_{i} ∣ < 1, i = 1, \dots, k$ . We pro…

math.DS2022★ 5 cited

Spectral cocycle for substitution tilings

Boris Solomyak, Rodrigo Treviño

The construction of spectral cocycle from the case of 1-dimensional substitution flows by Bufetov-Solomyak [arXiv:1802.04783] is extended to the setting of pseudo-self-similar tili…

math.DS2021

Self-similarity and spectral theory: on the spectrum of substitutions

Alexander I. Bufetov, Boris Solomyak

In this survey of the spectral properties of substitution dynamical systems we consider primitive aperiodic substitutions and associated dynamical systems: $Z$ -actions an…