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UID:2097@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20171222T110000
DTEND;TZID=Europe/Paris:20171222T120000
DTSTAMP:20171207T100000Z
URL:https://www.i2m.univ-amu.fr/evenements/hall-rays-for-lagrange-spectra-
 at-cusps-of-riemann-surfaces/
SUMMARY: (...): Hall rays for Lagrange spectra at cusps of Riemann surfaces
DESCRIPTION:: The Lagrange spectrum is a classical object in Diophantine ap
 proximation on the real line. It can be also seen as the spectrum of asymp
 totic penetration of hyperbolic geodesics into the cusp of the modular sur
 face. This interpretation yielded many generalizations of the Spectrum to 
 non-compact\, finite volume\, negatively curved surfaces and higher dimens
 ional manifolds. A remarkable property of the classical Spectrum is that i
 t contains an infinite interval\, called Hall ray. The presence of the Hal
 l ray is a common feature of the generalizations of the Lagrange spectrum 
 to higher dimensions. We show that the Lagrange spectrum of hyperbolic sur
 faces contains a Hall ray. Moreover\, we show that the same result holds i
 f we measure the excursion into the cusps with a proper function that is c
 lose in the Lipschitz norm to the hyperbolic height. This is a joint work 
 with L. Marchese and C. Ulcigrai.http://sites.google.com/sns.it/mauro-arti
 giani/
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