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SUMMARY:On continued fraction expansion of potential counterexamples to mi
 xed Littlewood conjecture. - Badziahin\, D (Durham University)
DTSTART:20140610T133000Z
DTEND:20140610T143000Z
UID:TALK52926@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Mixed Littlewood conjecture proposed by de Mathan and Teulie i
 n\n2004 states that for every real number $x$ one has\n$$\nliminf_{q	oinft
 y} qot |q|_Dot ||qx|| = 0.\n$$\nwhere $|*|_D$ is a so called pseudo norm
  which generalises the standard $p$-adic norm.\nIn the talk we'll consider
  the set $mad$ of potential\ncounterexamples to this conjecture. Thanks to
  the results of\nEinsiedler and Kleinbock we already know that the Haudorf
 f dimension\nof $mad$ is zero\, so this set is very tiny. During the talk 
 we'll\nsee that the continued fraction expansion of every element in $mad$
 \nshould satisfy some quite restrictive conditions. As one of them\nwe'll 
 see that for these expansions\, considered as infinite words\,\nthe comple
 xity function can neither grow too fast nor too slow.\n\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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