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SUMMARY:Gauss maps for simultaneous approximation - Cheung\, Y (San Franci
 sco State University)
DTSTART:20140703T090000Z
DTEND:20140703T095000Z
UID:TALK53304@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Levy's constant measures the exponential growth rate for the \
 nsequence of denominators of the convergents of a real number.  \nKhintchi
 ne proved existence for almost every real number and \nLevy computed the c
 onstant to be $pi^2/12ln2$.  This result \nis a standard exercise in moder
 n textbooks on ergodic theory.  \nIn this talk\, we generalize it to highe
 r dimensions with Levy's \nconstant defined using the sequence of best app
 roximation \ndenominators.  The main ingredient of the proof is constructi
 ng \nthe analog of the Gauss map for continued fractions.  This \nwork is 
 joint with Nicolas Chevallier.  \n\n
LOCATION:Seminar Room 1\, Newton Institute
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