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CATEGORIES:Ergodic Theory seminar
SUMMARY:Equidistribution of divergent orbits in the space
of lattices - Ofir David (Hebrew university\, Jer
usalem)
DTSTART;TZID=Europe/London:20180220T130000
DTEND;TZID=Europe/London:20180220T140000
UID:TALK101575AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/101575
DESCRIPTION: A well known application of the pointwise ergodic
theorem (PET) states that almost every x in [0\,1
] has a normal continued fraction expansion\, or e
quivalently its orbit under the Gauss map T(x):={1
/x} (where {y} is the fractional part of y) equidi
stributes with respect to the Gauss Kuzmin measure
dt/( ln(2)(1+t) ). This is not true for all x\, a
nd in particular it fails for rational numbers whi
ch have finite continued fraction expansions.\n\nI
n this talk we shall see how to "extend" the PET t
o rational numbers and its connection to divergent
orbits of the diagonal group in the space of 2-di
mensional lattices. Furthermore\, we shall show ho
w the natural setting of this problem is actually
over the adeles\, and in particular it can be form
ulated in any dimension (for which we give some pa
rtial results).\n\nThis is a joint work with Uri S
hapira from the Technion.\n
LOCATION:MR13 (EL.05)
CONTACT:HoD Secretary\, DPMMS
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