Let $\Psi=\{\psi_{n}\}_{n\geq1}$ be an iterated function system (IFS) on [0,1] with attractor $J.$ Associated with each $x\in J,$ there is a sequence $\{\omega_{n}(x)\}_{n\geq 1}$ consisting of integers, called the digit sequence of $x,$ such that
$x=\lim_{n\rightarrow\infty}\psi_{\omega_{1}(x)}\circ\cdots\circ \psi_{\omega_{n}(x)}$(1).
We revisit the Borel-Bernstein theorem in a $d$-decaying Gauss-like IFS, and completely characterize the metrical properties of the set
$E(\Phi)=\big\{x\in J\colon \omega_{n}(x)\geq \Phi(n) \text{ for infinitely many } n\in \mathbb{N}\big\},$
where $\Phi\colon \mathbb{N}\rightarrow \mathbb{R}$ is a positive function.
Saisai SHI1
,
Bo TAN2
,
*
,
Qinglong ZHOU3
. GROWTH RATE OF DIGITS IN A GAUSS-LIKE IFS[J]. Acta mathematica scientia, Series B, 2026
, 46(1)
: 293
-310
.
DOI: 10.1007/s10473-026-0117-2
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