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SUMMARY:Jiajie Zheng (University of North Texas)
DTSTART:20260319T161500Z
DTEND:20260319T173000Z
DTSTAMP:20260423T022916Z
UID:NEDNT/104
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/104/">
 Absolute-winning properties of equicontinuously-twisted badly approximable
  points in continued fractions and beta-transformations</a>\nby Jiajie Zhe
 ng (University of North Texas) as part of New England Dynamics and Number 
 Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIt is well know tha
 t in a $\\beta$-transformation system for an integer $\\beta>0$\, the set 
 ${x: \\liminf_{n\\to\\infty}|T^nx-y_n|>0}$ has full Hausdorff dimension fo
 r all sequences $(y_n)$ in $[0\,1)$ and in the Gauss map system ${x: \\lim
 inf_{n\\to\\infty}|T^nx-0|>0}$ also has full Hausdorff dimension. In this 
 talk\, I will introduce a dynamical approach to understanding these sets\,
  and the new technique will allow us to strengthen the results so that the
  “targets’’ can be generalized to any equicontinuous sequence of fun
 ctions\, enabling the targets to vary by trajectories. In particular\, not
 ably this will imply the full dimension of non-recurrent points\, bridging
  the problems of shrinking targets and Poincare recurrence.\n
LOCATION:https://researchseminars.org/talk/NEDNT/104/
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