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SUMMARY:Yufei Chen (TU Delft)
DTSTART:20221018T120000Z
DTEND:20221018T130000Z
DTSTAMP:20260423T021405Z
UID:OWNS/100
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/100/">M
 atching of orbits of certain $N$-expansions with a finite set of digits</a
 >\nby Yufei Chen (TU Delft) as part of One World Numeration seminar\n\n\nA
 bstract\nIn this talk we consider a class of continued fraction expansions
 : the so-called $N$-expansions with a finite digit set\, where $N\\geq 2$ 
 is an integer. For $N$ fixed they are steered by a parameter $\\alpha\\in 
 (0\,\\sqrt{N}-1]$. For $N=2$ an explicit interval $[A\,B]$ was determined\
 , such that for all $\\alpha\\in [A\,B]$ the entropy $h(T_{\\alpha})$ of t
 he underlying Gauss-map $T_{\\alpha}$ is equal. In this paper we show that
  for all $N\\in\n$\, $N\\geq 2$\, such plateaux exist. In order to show th
 at the entropy is constant on such plateaux\, we obtain the underlying pla
 nar natural extension of the maps $T_{\\alpha}$\, the $T_{\\alpha}$-invari
 ant measure\, ergodicity\, and we show that for any two $\\alpha\,\\alpha'
 $ from the same plateau\, the natural extensions are metrically isomorphic
 \, and the isomorphism is given explicitly. The plateaux are found by a pr
 operty called matching.\n
LOCATION:https://researchseminars.org/talk/OWNS/100/
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