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math.DS2025
On the Lyapunov spectrum of the twisted cocycle for substitutions
Boris Solomyak
The paper is devoted to the properties of a complex matrix ``twisted,'' otherwise called ``spectral,'' cocycle, associated with substitution dynamical systems. Following a recent f…
math.DS2024
A note on spectral properties of random -adic systems
Boris Solomyak
The paper is concerned with random -adic systems arising from an i.i.d. sequence of unimodular substitutions. Using equidistribution results of Benoist and Quint, we show in The…
math.DS2024
On nonlinear iterated function systems with overlaps
Boris Solomyak
We construct an example of an iterated function system on the line, consisting of linear fractional transformations, such that two of the maps share a fixed points, but the dimensi…