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UID:5137@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20171222T110000
DTEND;TZID=Europe/Paris:20171222T120000
DTSTAMP:20171207T100000Z
URL:https://www.i2m.univ-amu.fr/events/hall-rays-for-lagrange-spectra-at-c
usps-of-riemann-surfaces/
SUMMARY:Hall rays for Lagrange spectra at cusps of Riemann surfaces -
DESCRIPTION:The Lagrange spectrum is a classical object in Diophantine appr
oximation on the real line. It can be also seen as the spectrum of asympto
tic penetration of hyperbolic geodesics into the cusp of the modular surfa
ce. This interpretation yielded many generalizations of the Spectrum to no
n-compact\, finite volume\, negatively curved surfaces and higher dimensio
nal manifolds. A remarkable property of the classical Spectrum is that it
contains an infinite interval\, called Hall ray. The presence of the Hall
ray is a common feature of the generalizations of the Lagrange spectrum to
higher dimensions. We show that the Lagrange spectrum of hyperbolic surfa
ces contains a Hall ray. Moreover\, we show that the same result holds if
we measure the excursion into the cusps with a proper function that is clo
se in the Lipschitz norm to the hyperbolic height. This is a joint work wi
th L. Marchese and C. Ulcigrai.http://sites.google.com/sns.it/mauro-artigi
ani/
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DTSTART:20171029T020000
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