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SUMMARY:Karma Dajani (Universiteit Utrecht)
DTSTART:20240116T130000Z
DTEND:20240116T140000Z
DTSTAMP:20260423T021339Z
UID:OWNS/124
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/124/">A
 lternating N-continued fraction expansions</a>\nby Karma Dajani (Universit
 eit Utrecht) as part of One World Numeration seminar\n\n\nAbstract\nWe int
 roduce a family of maps generating continued fractions where the digit 1 i
 n the numerator is replaced cyclically by some given non-negative integers
  $(N_1\, \\dots\, N_m)$. We prove the convergence of the given algorithm\,
  and study the underlying dynamical system generating such expansions. We 
 prove the existence of a unique absolutely continuous invariant ergodic me
 asure. In special cases\, we are able to build the natural extension and g
 ive an explicit expression of the invariant measure. For these cases\, we 
 formulate a Doeblin-Lenstra type theorem. For other cases we have a more i
 mplicit expression that we conjecture gives the invariant density. This co
 njecture is supported by simulations. For the simulations we use a method 
 that gives us a smooth approximation in every iteration. This is joint wor
 k with Niels Langeveld.\n
LOCATION:https://researchseminars.org/talk/OWNS/124/
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