Abstract
We introduce a family of dynamical systems that generate negative !-expansions
and study the support of the invariant measure which is absolutely continuous with
respect to Lebesgue measure. We give a characterization of the set of digit sequences
that is produced by a typical member of this family of transformations. We discuss
the meaning of greedy expansions in the negative sense, and show that there is
no transformation in the introduced family of dynamical systems that generates
negative greedy. However, if one looks at random algorithms, then it is possible to
define a greedy expansion in base −[Beta].
| Original language | Undefined/Unknown |
|---|---|
| Pages (from-to) | #A5/1-#A5/18 |
| Number of pages | 18 |
| Journal | Integers : electronic journal of combinatorial number theory |
| Volume | 11B |
| Publication status | Published - 2011 |