1 results
Bernoulli decomposition and arithmetical independence between sequences
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 41 / Issue 5 / May 2021
- Published online by Cambridge University Press:
- 14 January 2020, pp. 1590-1600
- Print publication:
- May 2021
-
- Article
-
- You have access
- Open access
- Export citation
-
In this paper, we study the set
where
$$\begin{eqnarray}A=\{p(n)+2^{n}d~\text{mod}~1:n\geq 1\}\subset [0,1],\end{eqnarray}$$
$p$ is a polynomial with at least one irrational coefficient on non-constant terms, 
$d$ is any real number and, for 
$a\in [0,\infty )$, 
$a~\text{mod}~1$ is the fractional part of 
$a$. With the help of a method recently introduced by Wu, we show that the closure of 
$A$ must have full Hausdorff dimension.
