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SUMMARY:Yuru Zou (Shenzhen University)
DTSTART:20260324T130000Z
DTEND:20260324T140000Z
DTSTAMP:20260423T035956Z
UID:OWNS/164
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/164/">H
 ausdorff dimension of double base expansions and binary shifts with a hole
 </a>\nby Yuru Zou (Shenzhen University) as part of One World Numeration se
 minar\n\n\nAbstract\nFor two real bases $q_0\, q_1 > 1$\, a binary sequenc
 e $i_1 i_2 \\cdots \\in \\{0\,1\\}^\\infty$ is called the $(q_0\,q_1)$-exp
 ansion of the number\n\n\\[\n\\pi_{q_0\,q_1}(i_1 i_2 \\cdots) = \\sum_{k=1
 }^\\infty \\frac{i_k}{q_{i_1} \\cdots q_{i_k}}.\n\\]\nLet $\\mathcal{U}_{q
 _0\,q_1}$ denote the set of all real numbers having a unique $(q_0\,q_1)$-
 expansion. When the two bases coincide\, i.e.\, $q_0 = q_1 = q$\, it was s
 hown by Allaart and Kong (2019) that the Hausdorff dimension of the univoq
 ue set $\\mathcal{U}_{q\,q}$ varies continuously in $q$\, building on earl
 ier work of Komornik\, Kong\, and Li (2017). In this talk\, we will derive
  explicit formulas for the Hausdorff dimension of $\\mathcal{U}_{q_0\,q_1}
 $ and for the topological entropy of the associated subshift for arbitrary
  $q_0\, q_1 > 1$. We will also establish the continuity of these quantitie
 s as functions of the pair $(q_0\,q_1)$.\n
LOCATION:https://researchseminars.org/talk/OWNS/164/
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