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SUMMARY:Derong Kong (Chongqing University)
DTSTART:20230307T130000Z
DTEND:20230307T140000Z
DTSTAMP:20260423T040047Z
UID:OWNS/108
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/108/">C
 ritical values for the beta-transformation with a hole at 0</a>\nby Derong
  Kong (Chongqing University) as part of One World Numeration seminar\n\n\n
 Abstract\nGiven $\\beta \\in (1\,2]$\, let $T$ be the $\\beta$-transformat
 ion on the unit circle $[0\,1)$. For $t \\in [0\,1)$ let $K(t)$ be the sur
 vivor set consisting of all $x$ whose orbit under $T$ never hits the open 
 interval $(0\,t)$. Kalle et al. [ETDS\, 2020] proved that the Hausdorff di
 mension function $\\dim K(t)$ is a non-increasing Devil's staircase in $t$
 . So there exists a critical value such that $\\dim K(t)$ is vanishing whe
 n $t$ is passing through this critical value. In this paper we will descri
 be this critical value and analyze its interesting properties. Our strateg
 y to find the critical value depends on certain substitutions of Farey wor
 ds and a renormalization scheme from dynamical systems. This is joint work
  with Pieter Allaart.\n
LOCATION:https://researchseminars.org/talk/OWNS/108/
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