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SUMMARY:Vilmos Komornik (Université de Strasbourg)
DTSTART:20250923T120000Z
DTEND:20250923T130000Z
DTSTAMP:20260423T052838Z
UID:OWNS/152
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/152/">T
 opology of univoque sets in double-base expansions</a>\nby Vilmos Komornik
  (Université de Strasbourg) as part of One World Numeration seminar\n\n\n
 Abstract\nThis is a joint work with Yuru Zou and YiChang Li. Given two rea
 l numbers $q_0\,q_1>1$ satisfying $q_0+q_1\\geq q_0q_1$ and two real numbe
 rs $d_0\\ne d_1$\, by a double-base expansion of a real number $x$ we mean
  a sequence $(i_k)\\in \\{0\,1\\}^{\\infty}$ such that\n\\[\nx=\\sum_{k=1}
 ^{\\infty}\\frac{d_{i_k}}{q_{{i_1}}q_{{i_2}}\\cdots q_{{i_k}}}.\n\\]\nWe d
 enote by  $\\mathcal{U}_{{q_0\,q_1}}$ the set of numbers $x$ having a uniq
 ue expansion.\nThe topological properties of  $\\mathcal{U}_{{q_0\,q_1}}$ 
 have been investigated in the equal-base case  $q_0=q_1$ for a long time. 
 \nWe extend this research to the case  $q_0\\neq q_1$. \nWhile many result
 s remain valid\, a great number of new phenomena  appear due to the increa
 sed complexity of double-base expansions.\n
LOCATION:https://researchseminars.org/talk/OWNS/152/
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