BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Seul Bee Lee (Institute for Basic Science) DTSTART:20221115T130000Z DTEND:20221115T140000Z DTSTAMP:20260423T040001Z UID:OWNS/101 DESCRIPTION:Title: R egularity properties of Brjuno functions associated with by-excess\, odd a nd even continued fractions\nby Seul Bee Lee (Institute for Basic Scie nce) as part of One World Numeration seminar\n\n\nAbstract\nAn irrational number is called a Brjuno number if the sum of the series of $\\log(q_{n+1 })/q_n$ converges\, where $q_n$ is the denominator of the $n$-th principal convergent of the regular continued fraction. The importance of Brjuno nu mbers comes from the study of one variable analytic small divisor problems . In 1988\, J.-C. Yoccoz introduced the Brjuno function which characterize s the Brjuno numbers to estimate the size of Siegel disks. In this talk\, we introduce Brjuno-type functions associated with by-excess\, odd and eve n continued fractions with a number theoretical motivation. Then we discus s the $L^p$ and the Hölder regularity properties of the difference betwee n the classical Brjuno function and the Brjuno-type functions. This is joi nt work with Stefano Marmi.\n LOCATION:https://researchseminars.org/talk/OWNS/101/ END:VEVENT END:VCALENDAR