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UID:384@math.technion.ac.il

DTSTART;TZID=Asia/Jerusalem:20250120T123000

DTEND;TZID=Asia/Jerusalem:20250120T133000

DTSTAMP:20250115T160650Z

URL:https://math.technion.ac.il/events/extravagance/

SUMMARY:Extravagance\, irrationality and Diophantine approximation
DESCRIPTION:Lecturer:Jon Aaronson (TAU)\n Location:Amado 814\n \n\nDiophant
 ine approximation of irrationals is connected with the asymptotics  of th
 e Gauss transformation. For an invariant probability measure for the Gauss
  map\, almost all numbers are Diophantine (i.e.\, irrationality exponent=2
 ) if the log of the partial quotient function is integrable.\n\nWe show th
 at with respect to a continued fraction mixing measure for the Gauss map w
 ith the log of the partial quotient function non-integrable\, almost all n
 umbers are Liouville (i.e.\, irrationality exponent infinite).\n\nTime per
 mitting\, we'll also exhibit Gauss-invariant\, ergodic measures with arbit
 rary irrationality exponent and prove a Khinchin-type theorem for weak Ren
 yi measures.\n\n\nThe proofs are via  the "extravagance'' of non-negative
  stationary processes.\nWork in progress with Hitoshi Nakada. See arXiv:24
 09.19393 for preliminary version.\n 
CATEGORIES:Groups, Dynamics and Related Topics,Seminars
LOCATION:Amado 814

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