N. Sidorov

activity

19962022

most citedExpansions in non-integer bases: lower, middle and top orders

66 citations · 329 across the 36 of their papers we have counts for

collaborators

Showing 2008Show all

3 papers · 1 filter

math.DS2008★ 6 cited

A lower bound for Garsia's entropy for certain Bernoulli convolutions

Kevin G. Hare, Nikita Sidorov

Let $β \in (1, 2)$ be a Pisot number and let $H_{β}$ denote Garsia's entropy for the Bernoulli convolution associated with $β$ . Garsia, in 1963 showed that $H_{β} < 1$ for any Pisot $β$ . Fo…

math.DS2008

On the average growth exponent for beta-expansions

Nikita Sidorov

Let $\be\in(1,2)$. Each $x\in I_\be:=[0,\frac{1}{\be-1}]$ can be represented in the form \[ x=\sum_{k=1}^\infty a_k\be^{-k}, \] where $a_{k} \in {0, 1}$ for all $k$ (a $\be$-expansion…

math.DS2008

Periodic unique beta-expansions: the Sharkovskii ordering

Jean-Paul Allouche, Matthew Clarke, Nikita Sidorov

Let $β \in (1, 2)$ . Each $x \in [0, \frac{1}{β - 1}]$ can be represented in the form \[ x=\sum_{k=1}^\infty ε_kβ^{-k}, \] where $ε_{k} \in {0, 1}$ for all $k$ (a $β$ -expansion of $x$ ). If $β>…