Universal $β$-expansions
| dc.creator | Sidorov, Nikita | |
| dc.date | 2002-09-19 | |
| dc.date.accessioned | 2026-07-07T04:51:02Z | |
| dc.date.available | 2026-07-07T04:51:02Z | |
| dc.description | 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 related to the universality and combinatorics of $β$-expansions. Our main result is that for any $β\in(1,2)$ and a.e. $x\in (0,1)$ there always exists a universal $β$-expansion of $x$ in the sense of Erdös and Komornik, i.e., a $β$-expansion whose complexity function is $2^n$. We also study some questions related to the points having less than a full branching continuum of $β$-expansions and also normal $β$-expansions. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0209247 | |
| dc.identifier | http://arxiv.org/abs/math/0209247 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65004 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Number Theory | |
| dc.subject | 11A63; 11K16; 28D05 | |
| dc.title | Universal $β$-expansions | |
| dc.type | text |