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SUMMARY:Manfred Madritsch (Université de Lorraine)
DTSTART:20231003T120000Z
DTEND:20231003T130000Z
DTSTAMP:20260423T053137Z
UID:OWNS/118
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/118/">C
 onstruction of absolutely normal numbers</a>\nby Manfred Madritsch (Univer
 sité de Lorraine) as part of One World Numeration seminar\n\n\nAbstract\n
 Let $b\\geq2$ be a positive integer. Then every real number $x\\in[0\,1]$ 
 admits a\n$b$-adic representation with digits $a_k$. We call the real $x$ 
 simply\nnormal to base $b$ if every digit $d\\in\\{0\,1\,\\dots\,b-1\\}$ o
 ccurs with the same\nfrequency in the $b$-ary representation. Furthermore 
 we call $x$ normal to\nbase $b$\, if it is simply normal with respect to $
 b$\, $b^2$\, $b^3$\, etc.\nFinally we call $x$ absolutely normal if it is 
 normal with respect to all\nbases $b\\geq2$. \n\nIn the present talk we wa
 nt to generalize this notion to normality in measure\npreserving systems l
 ike $\\beta$-expansions and continued fraction expansions.\nThen we show c
 onstructions of numbers that are (absolutely) normal with respect\nto seve
 ral different expansions.\n
LOCATION:https://researchseminars.org/talk/OWNS/118/
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