8 papers
Spectra of Bernoulli convolutions as multipliers in on the circle
Nikita Sidorov, Boris Solomyak
It is shown that the closure of the set of Fourier coefficients of the Bernoulli convolution parameterized by a Pisot number , is countable. Combined with results of Salem…
Universal -expansions
Nikita Sidorov
Given , a -expansion of a real is a power series in base with coefficients 0 and 1 whose sum equals . The aim of this note is to study certain problems rel…
Ergodic-theoretic properties of certain Bernoulli convolutions
Nikita Sidorov
In [17] the author and A. Vershik have shown that for $\be=\frac12(1+\sqrt5)$ and the alphabet the infinite Bernoulli convolution ( the Erdös measure) has a property s…
Arithmetic Dynamics
Nikita Sidorov
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vec…
Bijective and general arithmetic codings for Pisot automorphisms of the torus
Nikita Sidorov
Let be an algebraic automorphism of having the following property: the characteristic polynomial of its matrix is irreducible over , and a Pisot nu…
On the fine structure of stationary measures in systems which contract-on-average
Matthew Nicol, Nikita Sidorov, David Broomhead
Suppose is a set of Lipschitz maps of . We form the iterated function system (IFS) by independently choosing the maps so that the map is chose…