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- W2241474562 abstract "In this article we study the first return map defined on the switch region induced by the greedy and lazy maps. In particular we study the allowable sequences of return times, and when the first return map is a generalised Luroth series transformation. We show that there exists a countable collection of disjoint intervals $(mathcal{I}_{n})_{n=1}^{infty},$ such that all sequences of return times are permissible if and only if $betain mathcal{I}_{n}$ for some $n$. Moreover, we show that there exists a set $Msubseteq(1,2)$ of Hausdorff dimension $1$ and Lebesgue measure zero, for which the first return map is a generalised Luroth series transformation if and only if $betain M$." @default.
- W2241474562 created "2016-06-24" @default.
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- W2241474562 date "2015-09-21" @default.
- W2241474562 modified "2023-09-24" @default.
- W2241474562 title "Induced Random $beta$-transformation" @default.
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