Optimal expansions in non-integer bases
| Autor: | Dajani, K., de Vries, M., Komornik, V., Loreti, P., Stochastics, Sub Stochastics and Decision Theory begr |
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| Přispěvatelé: | Stochastics, Sub Stochastics and Decision Theory begr |
| Rok vydání: | 2011 |
| Předmět: |
beta-expansion
greedy expansion Sequence Mathematics - Number Theory invariant measure Applied Mathematics General Mathematics ergodicity Dynamical Systems (math.DS) 11A63 37A05 37L40 Combinatorics FOS: Mathematics Interval (graph theory) Number Theory (math.NT) Mathematics - Dynamical Systems Mathematics Integer (computer science) |
| Zdroj: | Proceedings of the American Mathematical Society, 140(2), 437. American Mathematical Society |
| ISSN: | 1088-6826 0002-9939 |
| Popis: | For a given positive integer $m$, let $A=\set{0,1,...,m}$ and $q \in (m,m+1)$. A sequence $(c_i)=c_1c_2 ...$ consisting of elements in $A$ is called an expansion of $x$ if $\sum_{i=1}^{\infty} c_i q^{-i}=x$. It is known that almost every $x$ belonging to the interval $[0,m/(q-1)]$ has uncountably many expansions. In this paper we study the existence of expansions $(d_i)$ of $x$ satisfying the inequalities $\sum_{i=1}^n d_iq^{-i} \geq \sum_{i=1}^n c_i q^{-i}$, $n=1,2,...$ for each expansion $(c_i)$ of $x$. 11 pages, 0 figures, to appear in Proc. Amer. Math. Soc |
| Databáze: | OpenAIRE |
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