### The chordal norm of discrete Möbius groups in several dimensions.

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Let ${f\u2099}_{n\ge 1}$ be an infinite iterated function system on [0,1] satisfying the open set condition with the open set (0,1) and let Λ be its attractor. Then to any x ∈ Λ (except at most countably many points) corresponds a unique sequence ${a\u2099\left(x\right)}_{n\ge 1}$ of integers, called the digit sequence of x, such that $x=li{m}_{n\to \infty}{f}_{a\u2081\left(x\right)}\circ \cdots \circ {f}_{a\u2099\left(x\right)}\left(1\right)$. We investigate the growth speed of the digits in a general infinite iterated function system. More precisely, we determine the dimension of the set $x\in \Lambda :a\u2099\left(x\right)\in B\left(\forall n\ge 1\right),li{m}_{n\to \infty}a\u2099\left(x\right)=\infty $ for any infinite subset B ⊂ ℕ, a question posed by Hirst for continued...

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