N. Sidorov

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19982002

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math.DS2002

Universal $β$ -expansions

Nikita Sidorov

Given $β \in (1, 2)$ , a $β$ -expansion of a real $x$ is a power series in base $β$ with coefficients 0 and 1 whose sum equals $x$ . The aim of this note is to study certain problems rel…

math.DS2002

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 ${0, 1}$ the infinite Bernoulli convolution ( $=$ the Erdös measure) has a property s…

math.DS2002

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…

math.DS2000

Bijective and general arithmetic codings for Pisot automorphisms of the torus

Nikita Sidorov

Let $T$ be an algebraic automorphism of $T^{m}$ having the following property: the characteristic polynomial of its matrix is irreducible over $Q$ , and a Pisot nu…

math.DS1998

Bijective arithmetic codings of hyperbolic automorphisms of the 2-torus, and binary quadratic forms

Nikita Sidorov, Anatoly Vershik

We study the arithmetic codings of hyperbolic automorphisms of the 2-torus, i.e. the continuous mappings acting from a certain symbolic space of sequences with a finite alphabet en…

Universal β-expansions

Ergodic-theoretic properties of certain Bernoulli convolutions

Arithmetic Dynamics

Bijective and general arithmetic codings for Pisot automorphisms of the torus

Bijective arithmetic codings of hyperbolic automorphisms of the 2-torus, and binary quadratic forms

Universal $β$ -expansions