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 2013Show all

3 papers · 1 filter

math.DS2013★ 5 cited

On cycles for the doubling map which are disjoint from an interval

Kevin G. Hare, Nikita Sidorov

Let $T : [0, 1] \to [0, 1]$ be the doubling map and let $0 < a < b < 1$ . We say that an integer $n \geq 3$ is bad for $(a, b)$ if all $n$ -cycles for $T$ intersect $(a, b)$ . Let $B (a, b)$ denote the…

math.NT2013★ 1 cited

Expansions in non-integer bases: lower order revisited

Simon Baker, Nikita Sidorov

Let $q \in (1, 2)$ and $x \in [0, \frac{1}{q - 1}]$ . We say that a sequence $(ε_{i})_{i = 1}^{\infty} \in {0, 1}^{N}$ is an expansion of $x$ in base $q$ (or a $q$ -expansion) if…

math.DS2013★ 20 cited

The doubling map with asymmetrical holes

Paul Glendinning, Nikita Sidorov

Let $0 < a < b < 1$ and let $T$ be the doubling map. Set $J (a, b) := {x \in [0, 1] : T^{n} x \in / (a, b), n \geq 0}$ . In this paper we completely characterize the holes $(a, b)$ for which…